Questions on Algebra: Square root, cubic root, N-th root answered by real tutors!

Tutors Answer Your Questions about Square-cubic-other-roots (FREE)

Question 571451: Multiply.
(6+sqrt5)(6-sqrt5)
Answer by josmiceli(6772)

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+%28+6+%2B+sqrt%285%29+%29%2A%28+6+-+sqrt%285%29+%29+

+36+%2B+6%2Asqrt%285%29+-+6%2Asqrt%285%29+-+5+

You can check this:
+sqrt%285%29+=+2.23607+

+%28+6+%2B+2.23607+%29%2A%28+6+-+2.23607+%29+

close enough

Question 571216: Please help to solve this equation by completing the square:
3x^2 - x - 1 = 0
Answer by josmiceli(6772)

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+3x%5E2+-+x+-+1+=+0+

Take 1/2 of the coefficient of

, square it
and add it to both sides
+x%5E2+-%281%2F3%29%2Ax+%2B++%28-1%2F6%29%5E2+=+1%2F3++%2B+%28-1%2F6%29%5E2+

+x%5E2+-%281%2F3%29%2Ax+%2B+1%2F36+=+12%2F36+%2B+1%2F36+

Take the square root of both sides
+x+-+1%2F6+=+sqrt%28+13+%29+%2F+6+

and, also

-----------------------
check the solutions:
+3%2A%28+%28+1+-+sqrt%2813%29+%29+%2F+6+%29+%29%5E2+-+%28+1+-+sqrt%2813%29+%29+%2F+6+%29+-+1+=+0+

+%283%2F36%29%2A%28+1+-+2%2Asqrt%2813%29+%2B+13+%29++-+1%2F6+%2B+%28+sqrt%2813%29%29%2F6++-+1+=+0+

Multiply both sides by +12+

+1+-+2%2Asqrt%2813%29+%2B+13+-+2+%2B+2%2Asqrt%2813%29+-+12+=+0+

OK. You can check other solution

Question 570825: find the cube root of 108 x16 without actual muulitipliction
Answer by mananth(10539)

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cube root of 108 * 16
find prime factors
= cuberoot (2*2*3*3*3*2*2*2*2)
=12

Question 570400: whats the answer to y2-6y+9
Answer by Alan3354(21550)

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whats the answer to y2-6y+9
--------
What's the question?

Question 570276: (8+4)√2 = 19
Answer by JBarnum(1826)

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this is not an equation as 12sqrt%282%29=16.9706

not 19

Question 570008: 2x+9 squared
Answer by jim_thompson5910(21667)

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%282x%2B9%29%5E2

Start with the given expression.

%282x%2B9%29%282x%2B9%29

Expand. Remember something like x%5E2=x%2Ax

.

Now let's FOIL the expression.

Remember, when you FOIL an expression, you follow this procedure:

%28highlight%282x%29%2B9%29%28highlight%282x%29%2B9%29

%28highlight%282x%29%2B9%29%28highlight%282x%29%2B9%29

Multiply the First terms: %282%2Ax%29%2A%282%2Ax%29=4%2Ax%5E2

%28highlight%282x%29%2B9%29%282x%2Bhighlight%289%29%29

Multiply the Outer terms: %282%2Ax%29%2A%289%29=18%2Ax

%282x%2Bhighlight%289%29%29%28highlight%282x%29%2B9%29

Multiply the Inner terms: %289%29%2A%282%2Ax%29=18%2Ax

%282x%2Bhighlight%289%29%29%282x%2Bhighlight%289%29%29

Multiply the Last terms: %289%29%2A%289%29=81

.

---------------------------------------------------
So we have the terms: 4%2Ax%5E2

Now add every term listed above to make a single expression.

4x%5E2%2B36x%2B81

Now combine like terms.

So %282x%2B9%29%5E2

FOILs to

.

In other words, %282x%2B9%29%5E2=4x%5E2%2B36x%2B81

Question 570007: the square roots of 7 square
Answer by jim_thompson5910(21667)

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Use the idea that sqrt%28x%5E2%29=x

where x is some positive number to get sqrt%287%5E2%29=7

Question 569930: Im sooo confused i need help figuring this out!! please and thanks for helping:):)
1. Simplify the following expression; express in terms of i. Square root of -54
2. Simplify the following expression. square root of -14 and square root of -56
Answer by mananth(10539)

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sqrt%28-54%29

Question 569667: QUESTION 1
Please post a 150-300 word response answering all parts to the following question.
Quadratic equations may be solved by graphing, using the quadratic formula, completing the square, and factoring. What are the of each of these methods? When might each pros and cons method be most appropriate? Which method do you prefer? Explain why.

QUESTION 2
Please post a 150-300 word response to the following:
In your own words, explain how to solve a quadratic equation by completing the square. Demonstrate the process with your own example. Please explain step by step how you worked through your example.

Found 2 solutions by Alan3354, JBarnum:
Answer by Alan3354(21550)   (Show Source):
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QUESTION 1
Please post a 150-300 word response answering all parts to the following question.
Quadratic equations may be solved by graphing, using the quadratic formula, completing the square, and factoring. What are the of each of these methods? When might each pros and cons method be most appropriate? Which method do you prefer? Explain why.

QUESTION 2
Please post a 150-300 word response to the following:
In your own words, explain how to solve a quadratic equation by completing the square. Demonstrate the process with your own example. Please explain step by step how you worked through your example.
==============================================
We don't do that type of "problem" here.
We can't write in your own words.

Answer by JBarnum(1826)   (Show Source):
You can put this solution on YOUR website!
this is not a math question we cant answer. this is your opinion and your understanding of the processes and what you've learned and how they apply.
im not writing short paragraphs for your homework
Q1 first question unreadable and doesnt make sence. last question your opinion. you can find the definitions in the book
Q2 HINT "IN YOUR OWN WORDS" make up your own problem and solve it. nothing i can do for you dont ask these type of questions as this would be called cheating on your homework.

Question 569632: How do you factor this equation and solve for n in the following--
n squared minus n equals 20
n=5 but I am not sure how to get the answer other than by intuition--thanks
Answer by htmentor(580)   (Show Source):
You can put this solution on YOUR website!
How do you factor this equation and solve for n in the following--
n squared minus n equals 20
================================
n^2 - n = 20
n^2 - n - 20 = 0
Since -20 = -5*4 and -5 + 4 = -1, we can factor the equation as:
(n-5)(n+4) = 0
So the solutions are n=5, n=-4

Question 569554:
Show work so that I can see how you get the answer
Answer by JBarnum(1826)   (Show Source):
You can put this solution on YOUR website!

look for squares
squares shown then seperate below
square root of a square canceles out
add like terms

Question 569529:
I saw that your email address was attached to a Math Problem you solved at an earlier date on algebra.com. I was hoping you could help me with a problem I am having as well. Here is the problem, thank you in advance, if you cannot help me I understand :)

During the first part of a trip a canoeist travels 80 miles at a certain speed.
The canoeist travels 9 miles on the second part of the trip at a speed of 5 mph slower.
The total time for the trip is 4 hrs. What was the speed on each part of the trip?
Please provide exact answers for each part!
The speed on the first part of the trip was :__________ mph
The speed on the second part of the trip was:___________ mph
Simplify your answer. Type as integer or a decimal, round to the nearest hundredth

Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
During the first part of a trip a canoeist travels 80 miles at a certain speed.
The canoeist travels 9 miles on the second part of the trip at a speed of 5 mph slower.
The total time for the trip is 4 hrs. What was the speed on each part of the trip?
--------------
1st Part DATA:
distance = 80 miles ; rate = x mph ; time = d/r = 80/x hrs
-----
2nd Part DATA:
distance 9 miles ; rate = x-5 mph ; time = d/r = 9/(x-5) hrs
-----------------
Equation:
time + time = 4 hrs
80/x + 9/(x-5) = 4 hrs
---
Multiply thru by x(x-5) to get:
80(x-5) + 9x = 4x(x-5)
89x - 400 = 4x^2 - 20x
------
4x^2-109x+400 = 0
Usable positive solution:
x = 22.88 mph
===================
Cheers,
Stan H.

Question 569442: How do your figure out an equation where 1.058 is to the 20th power?
Answer by onlydabest503(3)   (Show Source):
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To find the answer you nave to multiply 1.058 by 1.058 twenty times. If you have another question about this problem then you can ask me.

Question 568805: A square has an area of 2.25 meters what is the measurement of each side in meters

Answer by sEahors3(4)   (Show Source):
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since this is the area of a square then the length and width will be the same..
and
Area = length * width
or we can say
Area = side1*side2
since they are the same we can say
Area = side * side
which also means
Area = side^2
so we have the area and we want the side, we need the inverse operation for squaring something. the inverse of squaring something is square rooting
so
sqrt(Area) = side
so
side = sqrt(2.25)
= 1.5 m

i feel like i made a short story long but i hope it helped =)

Question 568541: hello, i really didnt understand how to find the indicated roots of letters. here is my worksheet question 1:
Find the indicated nth root(s) of A
1.n=6, a=1,000,000
thank you for the help.
Answer by issacodegard(60)   (Show Source):
You can put this solution on YOUR website!
Hi, the nth root of A is the number x such that x^n=A. So, we need to find the number x such that x^6=1000000.
We can recognize that 1000000 is 10^6. So we have x^6=10^6. Raising to the 1/6 power on both sides give x=10, which is the 6th root of 1000000.

Question 568441: simplify square root of x squared minus 2x plus 1

Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Hint: is a perfect square trinomial and can be factored into

Question 568376: What is the square root of 125n?
Answer by Edwin McCravy(6931)   (Show Source):
You can put this solution on YOUR website!

Question 568138: What is the formula for finding the square root of 225? I know the answer is 15, I'm trying to figure out the formula, please. I know how to figure it using the factor tree, but I don't know how to do the square root formula Thank You so much!
P.S.
When I clicked on the drop down list to pick a topic, nothing came up. There were no words, just blank space & a check mark, so I'm sorry if the topic was off.

Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
There's not much of a formula. Square root is defined as "what number times itself equals the given number." Since 15*15 = 225, the square root of 225 is 15.

Question 567207: in the problem 3m^5-3m why is the answer 3m(m^2+1)(m+1)(m-1) instead of 3m(m+1)(m+1)(m+1)(m-1) ? I can not find any reason to have descending powers in factoring the difference of two squares??
Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!

You must have factored m^2 + 1 as (m+1)(m+1), which is incorrect. m^2 + 1 can't be factored into polynomials with real coefficients.

Question 566589: let me know how to find the cube root of 250
upto two decimal places
Answer by rfer(10417)   (Show Source):
You can put this solution on YOUR website!
=6.30

Question 566573: Evaluate What is the square root of b^2-4ac where a=2, b=-5, and c=-3
Answer by Maths68(1140)   (Show Source):
You can put this solution on YOUR website!
=
a=2, b=-5, and c=-3
=
=
=
=
= or

Question 566287: how do you solve y over 4 minus 6 equals negative 15?
Answer by ad_alta(170)   (Show Source):
You can put this solution on YOUR website!
1) (y/4)-6=-15 [add 6 to both sides]
2) y/4=-9 [multiply both sides by 4]
2)) y=-36

Question 565732: What Are two real solutions for x4=2401 over 625 ?
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
What Are two real solutions for x^4 = (2401/625) ?
x = (2401)^(1/4)/5
----
x = 7/5
x = 1.4
-----
The 2 answers are + or - 1.4
===================================
Cheers,
Stan H.

Question 565495: sqrt2^5 ......Im trying to ask...what is the square root of 2 to the 5th power? It cant be a decimal....how is this possible?
Found 2 solutions by scott8148, Alan3354:
Answer by scott8148(5879)   (Show Source):
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sure it's a decimal ___ but it's irrational (never ending)

[sqrt(2)]^5 = [sqrt(2)]^1 * [sqrt(2)]^4 = sqrt(2) * 2

Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
sqrt2^5 ......Im trying to ask...what is the square root of 2 to the 5th power? It cant be a decimal....how is this possible?
---------

=

Question 565277: Please help me simplify cube root of
Answer by mananth(10539)   (Show Source):
You can put this solution on YOUR website!

Question 564949: why is math so difficult? please answer ASAP. thanks (:
Logan(:
Answer by Alan3354(21550)   (Show Source):
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why is math so difficult?
---------
It's only difficult if you don't know how to do it.
-----
Maybe you can recall doing math a few years ago, when fractions seemed difficult, for example. Once you know how, it's easy.
------
On the positive side, math is dependable. The results are constant, not subject to opinions, or changing with how many vote for 4 vs. how many vote for 5.
--------
A lot of people think speaking Swedish is hard, but there are kids in Sweden not even 5 yrs old that speak it.

Question 564950: we learn units after units in Math class...but when are we ever going to use this in real world situations? i mean when are we going to need to know that the cubed root of fourteen plus twelve equals x minus fifteen? i mean....get real. i need an answer soon. thanks(:

Sincerely,
Logan-Ann Wetzbarger
Answer by Alan3354(21550)   (Show Source):
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we learn units after units in Math class...but when are we ever going to use this in real world situations? i mean when are we going to need to know that the cubed root of fourteen plus twelve equals x minus fifteen? i mean....get real.
---------------
It depends on what you do later. The real-world math problems are a LOT harder than the cube roots.
If you have no intention of doing anything more technical than checking on a bank account, then it's hard to justify some of the math classes. It's not my idea for you to have to take the classes.
But, if you learn something, it does increase your overall knowledge, and the brain seems to improve with exercise and use.

Question 564946: what is 8√50 - 3√32 ?
Answer by issacodegard(60)   (Show Source):
You can put this solution on YOUR website!
Let's simplify the square roots as much as possible:

Similarly,

So we get,

Question 564808: 3square root54
Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
3square root54
----------

Question 564746: 7×t√=360
Answer by Theo(2967)   (Show Source):
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i'm not exactly sure what you're asking.
you may be asking:
7 * sqrt(t) = 360
in that case, you would divide both sides of that equation by 7 to get:
sqrt(t) = 360/7
you would then square both sides of this equation to get:
t = (360/7)^2 which is equivalent to:
t = 360^2 / 7^2 which would be equivalent to:
t = 129600 / 49.
that can't be simplified further so that's your anser.
in decimal form, that answer would be:
t = 2644.897959
if that's not what you were looking for, then send me an email with what you were really looking for in english.,
something like:
7 times the square root of (t) = 360 would be an english equivalent of what i thought the problem was.

Question 564613: x-squared + 10x - 7 = 0 , completing the square
Answer by ad_alta(170)   (Show Source):
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1) x^2+10x-7=0
2) [x+(5)]^2=7+25
3) x+5= [+/-] (32)^(1/2)
4)x= -5 [+/-] 4*sqrt(2)

Question 564503: im trying to do
Answer by TutorDelphia(189)   (Show Source):
You can put this solution on YOUR website!
To do this problem remember that
we need to find a common denominator to add to a fraction.
Currently we have so we need to multiply the first fraction by which will give us
which would be
now generally its bad form to leave a square root on the bottom so we can multiply by again

You can check on your calculator that what you started with and ended with have the same value (around 5.196)

Question 563745: squared (4x+1)=squared ((squareroot(x-2)) +3)
Answer by nyc_function(2626)   (Show Source):
You can put this solution on YOUR website!
Do you mean: sqrt{4x = 1} = (sqrt{(x - 2) + 3)}^2

Square both sides of the equation.
This will remove the radical.

Can you take it from here?
Watch this video clip to learn how to solve such questions.

http://www.youtube.com/watch?v=a4bG_in_p_I

Question 563714: Hi I need help solving this:
It's the last step of my geometric problem, but I have no idea how to multiply that!? Please help me, thank you.
Answer by Tatiana_Stebko(1060)   (Show Source):
You can put this solution on YOUR website!

Question 563659: how to simplify the square root of 216
Answer by josmiceli(6772)   (Show Source):
You can put this solution on YOUR website!

answer

Question 561701: what is the answer to this equation 2 cubed times 3 squared plus 3 times 14 minus 4
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
2 cubed times 3 squared plus 3 times 14 minus 4
----
2^3*3^2+3*14-4
----
8*9+42-4
---
72 + 38
---
= 110
============
Cheers,
Stan H.

Question 559492: √63 + √7 + √64 = ?
The correct answer is 4√7 + 8, but I can't figure out how to get it.
Thanks
Found 2 solutions by richard1234, Earlsdon:
Answer by richard1234(4789)   (Show Source):
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Answer by Earlsdon(6098)   (Show Source):
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Simplify:

=
or so...
= or

Question 559515: add or subtract the square root of 108x - the square root of 27x
Answer by Theo(2967)   (Show Source):
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sqrt(108x - sqrt(27x) equals:
sqrt(36*3x) - sqrt(9*3x) equals:
6*sqrt(3x) - 3*sqrt(3x) equals:
(6-3)*sqrt(3x) equals:
3*sqrt(3x)
confirm by assigning a value to x and solve in the original equation and in the final equation to see that both equations give you the same answer.
use your calculator.
for example:
let x = 32 (random number picked out of the air).
when x = 32, the original equation becomes:
sqrt(108*32) - sqrt(27*32) which becomes:
sqrt(3456) - sqrt(864) which becomes:
29.39387691
when x = 32, the final equation becomes:
3*sqrt(3*32) which becomes:
3*sqrt(96) which becomes:
3*9.797958971 which becomes:
29.39387691
the original equation and the final equation both get the same answer so it looks like the simplification went well.
the simplified expression is:
3*sqrt(3x)

Question 559494: √y^3 can be written as (y^3)1/2 or (y)3/2.
GIven this, what does (8)5/3 equal?
The correct answer is 32, but I can't figure it out.
Please help me.
Thanks
Answer by KMST(576)   (Show Source):
You can put this solution on YOUR website!
= = = = = = = = 32
Some of the too-tall exponents are not wholly visible, but I included plenty of equivalent expressions to help you figure them out.

Question 558967: x^2-2x-8/x^2-x-6
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
x^2-2x-8/x^2-x-6
----
Factor to get:
[(x-4)(x+2)] / [(x-3)(x+2)]
----
Cancel the common (x+2) factors:
---
= (x-4)/(x-3)
==================
Cheers,
Stan H.

Question 558893: 5x^2-6=0
Answer by Edwin McCravy(6931)   (Show Source):
You can put this solution on YOUR website!
5x² - 6 = 0 Add 6 to both sides 5x² = 6 Divide both sides by 5 x² = x = Rationalize the denominator by multiplying inside the radical by to make the denominator become a square: x = x = x = Edwin

Question 558894: use the square root property to solve the equation

(x+1)^2=9

2) x^2=121
Answer by Theo(2967)   (Show Source):
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problem 1:
(x+1)^2 = 9
take the square root of both sides of this equation to get:
x+1 = 3
subtract 1 from both sides of this equation to get:
x = 2
problem 2:
x^2 = 121
take the square root of both sides of this equation to get:
x = 11