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

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 Algebra: Square root, cubic root, N-th root Solvers Lessons Answers archive Quiz In Depth

Question 703460: Square root of 3 times the square root of three times the square root of four
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Using the application of surd.
Sqt3 x sqt3 x sqt4
sqt3 x sqt3=sqt9
sqt9=3
sqt4=2
so therefore
3 x 2=6

Question 751329: I need to know more about Algebra to pass the ASVAB test to enter the military
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I need to know more about Algebra to pass the ASVAB test to enter the military

I can recommend you to a specialist. Besides tutoring the ASVAB, she's a veteran. She specializes in online tutoring which is quite convenient for most, and resides in Brooklyn, NY.

E-Mail me if you want her info.

You can do the check!!

Question 751196: what is the real cubic square root of square root 80n to the fifth power ?
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Please repost with clearer instructions (do you mean cube roots or square root - they are different and I've never heard of a cubic square root)

:)

Question 751038: solve x - sqrt15-2x = 0
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solve x - sqrt15-2x = 0
x=-√15
x^2=15
x=±√15

Question 751034: solve x - 2 sqrt(x) = 35
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solve x - 2 sqrt(x) = 35
x-2√x=35
let u=√x
u^2=x
u^2-2x-35=0
(u-7)(u+5)=0
u=7=√x
x=49
check:49-2√49=49-14=35
..
u=-5=√x
x=25
check:25-2√25=25-10=15 (extraneous root)

Question 750728: cube root of 368

I need to find x.

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x^3= 716.2

(x^3)^(1/3)= (716.2 )^(1/3) ... raise both sides to the 1/3 power

x = (716.2 )^(1/3)

x = 8.94701376606746 ... Use a calculator to evaluate the right side (this is approximate)

Question 750194: Find the distance between d(P1, P2) between the points P1 and P2.
P1 = (3, -4); P2 = (5, 4)

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Find the distance between d(P1, P2) between the points P1 and P2.
P1 = (3,-4); P2 = (5,4)
------------

Question 750116: what is the square root of 841 i am stuck i am not getting the answer i am getting
42 an if you got the answer pls tell me th method

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is close to and a little less than

makes
so and

NOTE:
For other numbers, you could get at the answer by doing a prime factorization.

Question 750094: Solve
SR (2x+6)=2SRx

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SR (2x+6)=2SRx
squaring both side we will get
2x+6=4x
6=4x-2x
6=2x
x=3

Question 749362: how do i solve this equation √(6x+4)=7

Question 748609: i am having difficulty understanding simplifying plobems such as 3(squarerootof)28. the fewer simple steps the better. thank you for your time
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i am having difficulty understanding simplifying plobems such as 3(squarerootof)28. the fewer simple steps the better. thank you for your time

------ Factoring the RADICAND, ensuring that one of the factors is a PERFECT SQUARE

Question 747402: what is the square root of y to third power?

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SQRT(Y^3)=Y SQRT(Y) ANS.

Question 746981: What value of c makes x^2+24x+c contain a perfect square trinomial
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Take half of the x coefficient 24 and square it to get (24/2)^2 = 12^2 = 144

So c = 144

Question 746947: how to find the root of 1
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SQRT1=1
PROOF
1^2=1

Question 746927: Please solve this problem ASAP. I have a test tomorrow and I am doing extra practice to prepare. I completed this problem, but I am unsure if I did it correctly. Thanks in advance for helping me. Complete the square of the following problem: 2x^2 - 4x - 3 = 0
I got the answer: x = 1 +/- sqrt5/2
*+/- = positive negative
*sqrt = square root

Found 2 solutions by josmiceli, jim_thompson5910:
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Take 1/2 of the co-efficient of x,
square it and add it to both sides

Take the square root of both sides

and also,

---------------------
I think you were correct
You can plug these answers back into the
original equation as a check- I'll leave it to you.

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or

or

or

or

or

or

or

or

So the two solutions are or

Question 746932: Please solve this problem ASAP. I have a test tomorrow and I am doing extra practice to prepare. I completed this problem, but I am unsure if I did it correctly. Thanks in advance for helping me. Complete the square of the following problem: 2x^2 = 4x - 5
I got the answer: x = 1 +/- i sqrt3/2
*+/- = positive negative
*sqrt = square root
*i = fake number system was used

Found 3 solutions by rothauserc, Alan3354, josgarithmetic:
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Complete the square of the following problem: 2x^2 = 4x - 5
2x^2 - 4x = 5
x^2 - 2x = 5/2
add 1 to both sides and we get
x^2 - 2x + 1 = 5/2 + 1 and
(x-1)^2 = 7/2
x-1 = sqrt(7/2)
x = 1+sqrt(7/2) = 1 + 1.9 = 2.9
x = 1-sqrt(7/2) = 1 - 1.9 = -.9

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Complete the square of the following problem: 2x^2 = 4x - 5
--------------
I think you mean solve for x by completing the square.

-------------

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Your solution for x does not indicate your knowing about Completing the Square. Showing some of your work for Completing the Square would be better than just showing what x is.

What must be added to the rectangular expression to make the result into a square expression? You will need . Add 1 inside the parentheses and subtract outside of the parentheses. From that, you have other calculations and simplifications. Your turn.

----I should include, the reason 1 will complete the square is because you have as the "rectangular" expression and that is what you want to use in making a square trinomial, which can then be factored. The "2" used is the "b" which is generally used as , the term which is added to Complete the Square.

Question 746746: how do you solve the multiplication of the square root 125 times the square root of 125

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Square root 125 x square root 125
= 125
If you put square root in index form
you have 125^1/2 x 125^1/2
As you add indices when multiplying

Question 746042: I have to solve the formula for volume of a cylinder where d=square over 4v divided by symbol pie and h?
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I have to solve the formula for volume of a cylinder where d=square over 4v divided by symbol pie and h?
-------------
It's not clear what you mean.
For a cylinder,

Question 744348: What is the solution of the equation?

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-----

x = 4*3^(3/8) - 2

Question 744346: What is the solution of the equation?

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square both sides
x=2
try it
it works

Question 743514: Solve by the square root property
25(y+5)^2=81

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or

Solving the two equations we get
y=-16/5 or y=-34/5

Question 743350: Trying to solve 2*sqrt(x-3)=6
tried squaring both sides and came up with 2*x-3 = 6^2
that divided out to X=21
tried checking the answer but it does not work.
Is this equation not solvable?
Thank you..

You can put this solution on YOUR website!
2*sqrt(x-3)=6}}}
/2

square both sides
x-3=9
x=12
( when you have squared you have to square the 2also)

Question 743127: Simplify Square root of 45k^7q^8
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SQRT(45 k^7 q^8)
SQRT(9*5 k^6*k q^4*q^4)
3 k^3 q^4sqrt(5 k)

Question 742662: 5/sqrt( 10x )
Please help me rationalize the denominator to simplify this! Can you tell me how? I answered the question and already got it wrong, I am just reviewing. Thank you so much I REALLY appreciate it!

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5/sqrt( 10x )
--------
Multiply numerator and denominator by sqrt(10x) to get:
= [5*sqrt(10x)/(10x)
--------
= (5/10)(sqrt(10x)/x)
--------
= (1/2)sqrt(10x)/x
=======================
Cheers,
Stan H.
=================

Question 741952: 8 devided by the square root of 3
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8 divided by the square root of 3
--------
8/sqrt(3) = [8sqrt(3)/3] = (8/3)sqrt(3)
==============================
Cheers,
Stan H.
==============================

Question 740163: what is the square root of 600a over 4b cubed? and can you please show the work so i can see how you got the answer? please and thank you.
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we are given
sqrt(600a) / (3b)^3
this equation is equal to
sqrt(600)*sqrt(a) / 64b^3
which equals
24.50*sqrt(a) / 64b^3
which is .38*sqrt(a) / b^3

Question 740065: thirty times the square root of a non zero number is equal to 8 times the number.

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let a non zero number be
times the square root of a non zero number is
equal to times the number is
so, we have
...you can solve for if you square both sides

....use zero product rule
if ..this is a solution, but our number should be non zero; so, we need other solution
or if => => =>
so, a non zero number be and this is your solution
let's check this solution:

.....this confirms that our answer is correct

Question 739957: I need help! what does x to the power of minus 3 equal? and how do i work it out?!
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The general rule is:

-------------------
and
, so

-------------------
Also, the negative exponents operate
just the positive exponents.
A general rule is:

then

, so

-------------------
Following the general rule,

--------------------
hope this helps

Question 739760: I don't know how to solve this. b^2-5=-8 What is the square root if it can't be negative?
Answer by Edwin McCravy(8909)   (Show Source):
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```It's imaginary!  Have you studied imaginary numbers?
If you haven't, you should say this "has no REAL solutions".
But if you have studied imaginary (NON-REAL) numbers,
you should do this:

b˛ - 5 = -8
b˛ = -3
b = ±√-3
b = ±i√3

Edwin```

Question 739524: distance between (-2,-1) and (3,4)
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For more help and practice with distance formula problems, check out this distance formula solver.

 Solved by pluggable solver: Distance Formula The first point is (x1,y1). The second point is (x2,y2) Since the first point is (-2, -1), we can say (x1, y1) = (-2, -1) So , Since the second point is (3, 4), we can also say (x2, y2) = (3, 4) So , Put this all together to get: , , , and -------------------------------------------------------------------------------------------- Now use the distance formula to find the distance between the two points (-2, -1) and (3, 4) Plug in , , , and ========================================================== Answer: The distance between the two points (-2, -1) and (3, 4) is exactly units The approximate distance between the two points is about 7.07106781186548 units So again, Exact Distance: units Approximate Distance: units

For more help and practice with distance formula problems, check out this distance formula solver.

Question 739215: Please help me solve this equation: I cant get a single value for x is it even possible?
Found 2 solutions by MathLover1, richwmiller:
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.....raise both sides to power of

...raise both sides to power of again

solutions:

.......since we need , this is not solution for your problem because

......here and this is your solution
so, is true for

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sqrt( x + sqrt(x))= sqrt(30)
x + sqrt(x)= 30
25+5=30
x=25

Question 738388: sqrt(2x+3)-sqrt(x+1)=1
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....raise both side to power of

solutions
if , the
if , the

Question 737606: I am dying here!!
I have negative three-fifths cubed. The other one that I'm stuck on is the fourth root of 256 over 81. I am not good at math.

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"Cubed" means .

"Negative three-fifths cubed", is
=.

(4x)^2 + sqrt(2x+3) = 8x + 1
Thanks a lot, i'm really appreciate your help!

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(4x)^2 + sqrt(2x+3) = 8x + 1
----
sqrt(2x+3) = -4x^2+8x+1
---
2x+3 = (-4x^2+8x+1)(-4x^2+8x+1)
-----
2x + 3 = 16x^4-32x^3-4x^2 -32x^3+64x^2 + 8x - 4x^2+8x+1
2x+3 = 16x^4 - 64x^3 + 56x^2 + 16x + 1
----
16x^4 - 64x^3 + 56x^2 + 14x -2 = 0
----
8x^4 - 32x^3 + 28x^2 + 7x - 1 = 0
--------------
I graphed it and found zeroes at
x = -0.28.., x = +0.104.., x = 1.78.. and x = 2.40...
------
Check for extraneous zeroes.
Cheers,
Stan H.
================

Question 737082: Hello, I need to know what is the square root of 36. I really don't understand how to solve this math problem.
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Basic multiplication fact. What do you find on the multiplication table? Look at the main diagonal and you will see the number multiplied by itself. The reason, "square" is used is because this is the way to find area for a square. A figure with one dimension at right angle to the other dimension and both dimensions are the same size, is SQUARE.

If you take 36 squares, and arrange them on a flat surface to form the shape of a larger square, the HOW MANY OF THESE SMALL SQUARES ARE ON EACH SIDE OF THE LARGER SQUARE COMPOSED OF THESE 36 SQUARE PIECES? The answer is 6.

With that example, you have a row of 6 squares arranged in 6 columns and altogether they are 36 pieces. See the basic fact, . THAT is squaring.

What you want to answer is, What is the number n, so that ? You are asking for the square root of 36. The square root of 36 is 6.
, because .

Question 736752: What is the fifth root of -1-i
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What is the fifth root of -1-i
------------
There are 5 of them.
----
|z| = sqrt(2)
-1-i --> z = sqrt(2)cis(225)
, n = 0, 1, 2, 3, 4

(1.2)sq root + (2.8)sq root =3.1. How do yu calculate to get the answer 3.1This is what i did
1.2 x1.2= 1.44
2.8 x 2.8 = 7.84
1.44 + 7.84 = 9.28
here is where i am not sure how to get to the answr which is 3.1

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Are you using ?
That is simply wrong.

In fact, as any good approximation to nearest tenth.

Try just using a handheld calculator:
Find and find . Now sum them. What do you find?

(1.2)2 + (2.8)2= 9.28(2)=3.1 I am not sure how to compute 9.2 sq to equal 3.1

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Too many equal signs.
Cheers,
Stan H.

Question 736227: 2 square root of 8
but then what?

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2 square root of 8
but then what?
-------------
idk. What did you want to do?

Question 736035: what is the square root of 3 times the cube root of nine? 3 to the 1/2 times 9 to the 1/3? I don't see how the exponents are manipulated to yield the answer 9 to the 7/12!