Questions on Algebra: Radicals -- complicated equations involving roots answered by real tutors!

You can put this solution on YOUR website!

Its NOT
Answer:

You can put this solution on YOUR website!
h = V / (r^2 * pi)

r^2 = V / (h * pi)

r = sqrt[V / (h * pi)]

You can put this solution on YOUR website!
V = pi * r^2 * h

314 = 3.14 * 25 * h

You can put this solution on YOUR website!
the answer for your question is (9x/y) cube root of x to the power of 2.

You can put this solution on YOUR website!

Start with the given expression



The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 686


Factors:
1, 2, 7, 14, 49, 98, 343, 686


Notice how 49 is the largest perfect square, so lets factor 686 into 49*14


Factor 686 into 49*14

Break up the square roots using the identity

Take the square root of the perfect square 49 to get 7

So the expression simplifies to

----------------------------
Check:
Notice if we evaluate the square root of 686 with a calculator we get



and if we evaluate we get



This shows that . So this verifies our answer

You can put this solution on YOUR website!

Start with the given expression



The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.


So let's list the factors of 686


Factors:
1, 2, 7, 14, 49, 98, 343, 686


Notice how 49 is the largest perfect square, so lets factor 686 into 49*14


Factor 686 into 49*14

Break up the square roots using the identity

Take the square root of the perfect square 49 to get 7

So the expression simplifies to

----------------------------
Check:
Notice if we evaluate the square root of 686 with a calculator we get



and if we evaluate we get



This shows that . So this verifies our answer

You can put this solution on YOUR website!
How do you solve ^16 sqrt -7^16?
-------------
It's not an equation, and there's no variable, so there's nothing to solve.
----
What does ^16 mean?
If it's the 16th root:

= 7 or -7
---------
If you expand (-7)^16, you get a big positive integer.
Then there are 16 16th roots of it, ± 7 being the most obvious.
-------
If you take = then it's -7.

You can put this solution on YOUR website!
x
x

You can put this solution on YOUR website!
I find that a minus sign is easier to deal with if I see it as part of the number that follows it. If I do not see a number, the number is an invisible 1. So for , I see . And for , I see .
For the problem above, I prefer to believe that I am seeing

I do not write it that way, but I see it that way in my mind, and that helps me keep the signs straight.

Otherwise, you have to remember (and hopefully justify to yourself) that to eliminate a set of brackets right after a minus sign, you also have to reverse all the signs inside the brackets, so that -(6x+2)=-(+6x+2) turns into .

You can put this solution on YOUR website!
Which is the better buy?
16oz bottle of lotion for $2.39
239/16 = 14.9375 cents per oz.
or
24oz bottle of lotion for $3.24?
324/24 = 13.5 cents per oz.
================
cheers,
Stan H.
=========

You can put this solution on YOUR website!

               

Isolate one radical term on one side:

                   = 

                 = 


     - 8 + 16 = 2x - 10

    3x + 1 - 8 + 16 = 2x - 10

        3x - 8 + 17 = 2x - 10

Isolate the radical term on one side:

                  x + 27 = 8

Square both sides:

               (x + 27)² = 8²

          x² + 54x + 729 = 64(3x + 1)

          x² + 54x + 729 = 192x + 64

Get 0 on the right:

         x² - 138x + 665 = 0         

Factor:

        (x - 5)(x - 133) = 0

Use the zero factor principle:

    x - 5 = 0        x - 133 = 0 
        x = 5              x = 133

We much check all solution because squaring both sides
often but not always introduces extraneous answers.

Checking x = 5 in the original:





4 - 0 = 4
    4 = 4

So x = 5 is a solution.

Checking x = 133 in the original:





20 - 16 = 4
      4 = 4

So x = 133 is also a solution.

Edwin

You can put this solution on YOUR website!
sqrt ( 3x )+ sqrt ( 2x-1 ) = 5 / sqrt ( 2x-1 )
√3x+√(2x-1)=5/√(2x-1)
multiply both sides by √(2x-1)
√(6x^2-3x)+2x-1=5
√(6x^2-3x)=-2x+6
square both sides
6x^2-3x=4x^2-24x+36
2x^2+21x-36=0
(x+12)(2x-3)=0
x=-12
or
x=3/2

You can put this solution on YOUR website!
between which two consecutive integers is the cube root is 11
------------
That makes no sense.

You can put this solution on YOUR website!
4th root of 8 times the 4th root of 16 divided by the 8th root of 2 times the 8th root of 3
----
= [ 2^(3/4)*2^(4/4)] / [2^(1/8)*3^(1/8)]
-------
= [2^(3/4)]/[6^(1/8)]
-------
= [2^(6/8)] / [6^(1/8)]
-------
= [2^6*6]^(1/8)
---
= (64*6)^(1/8)
----
= 384^(1/8)
---
= 2.1040
==============
Cheers,
Stan H.
=============

You can put this solution on YOUR website!
you have g(x) = sqrt(-x)
when y = 3, x = -9
when y = 2, x = -2
when y = 1, x = -1
presumably, you are given the value of g(x) which you also call y.
that's ok because you would then have y = g(x) = sqrt(-x) which is valid.
supposed you are first given that y = 3.
your equation of y = sqrt(-x) becomes:
3 = sqrt(-x)
you would square both sides of this equation to get:
9 = (sqrt(-x))^2 which becomes:
9 = -x
you then multiply both sides of the equation by -1 to get:
-9 = x which is the same as:
x = -9
for your information, the square root of (-x) is only imaginary when x is positive.
when x is negative, the square root of (-x) becomes the square root of a positive number because minus a negative number results in a positive number.
the same process is used to solve for the other values.
you are given 2 = sqrt(-x)
squareboth sides to get:
4 = (sqrt(-x))^2 which becomes:
4 = -x which then becomes
x = -4 after multiplying both sides of the equation by -1.
additional information for you:
sqrt(-x) is the same as (-x)^(1/2)
your equation of:
2 = sqrt(-x) can also be written as:
2 = (-x)^(1/2)
square both sides of this equation to get:
4 = ((-x)^(1/2))^2 which results in:
4 = (-x)^((1/2)*2) which becomes:
4 = (-x)^(1) which becomes:
4 = -x which then becomes:
x = -4 after multiplying both sides of the equation by -1.

You can put this solution on YOUR website!
How does 5 times the fourth root of r cubed divided by the square root of r simplify to 5 times the fourth root of r?
-------
5*r^(3/4)/(r^(1/2))
----
= 5[r^((3/4)-(1/2))]
-------
= 5[r^((3/4)-(2/4)]
---
= 5[r^(1/4)]
----
= 5*4th root of r
==========================
Cheers,
Stan H.
=============

You can put this solution on YOUR website!
square root of y+8 minus square root of y-6 equals -3,
:
= -3
:
- 3
square both sides
y + 8 = [ - 3]^2
FOIL the right side
y + 8 =
:
y + 8 = y + 3 -
:
y + 8 = y + 3 -
y - y + 8 - 3 =
5 =
square both side again
25 = 36(y-6)
25 = 36y - 216
25 + 216 = 36y
241 = 36y
y =
y = 6.7 which about what you got, but the trouble is if we substitute this in the original problem we get a +3 not -3, therefore there is no solution

You can put this solution on YOUR website!
i^11 (24/4i^5)

i know that i^11= i but as far as the steps to take in order to simplify the equation I get lost.
---------------

= -6
---------------

====================
i^11 (24/4i^5)

i know that i^11= i but as far as the steps to take in order to simplify the equation I get lost.
There is no equation. No equal sign --> not an equation.

You can put this solution on YOUR website!
7n^2=-4n
-----

n(7n + 4) = 0
n = 0
n = -4/7

You can put this solution on YOUR website!
How'd you get x=20 from x^2 - x = 20?

You should also subtract the 20, so your equation will look something like

, this factors to

, so x = 5 or x = -4. Since we have a square root, we should check to make sure our solutions actually work. x = 5 definitely works, x = -4 probably won't since the square root usually denotes only the positive root. The solution 13/12 is wrong.

You can put this solution on YOUR website!

You can put this solution on YOUR website!
It's true.
Also,

You can put this solution on YOUR website!
Explain the difference between rationalizing the denominator in an algebraic expression whose denominator has only one term involving a radical and one whose denominatror has two terms, at least one of which involves a radical.
**
For one-term radicals in the denominator, multiply top and bottom by the radical itself.
For two-term radicals in the denominator, multiply top and bottom by the conjugate to get a difference of two squares to eliminate the radicals.
Remember, we only talking about radicals with index of 2 or square roots. To rationalize terms with radicals of other than index 2, a different method is required.

You can put this solution on YOUR website!

Factor to reveal a perfect square and -1

we know the square root of -1 = i, and the square root of 16 = 4 so we have:

or some would write it

You can put this solution on YOUR website!
What is the answer to
you know the square root of 16 is 4, factor the square root of 8 to reveal a perfect square:
4 +
Extract the square root of 4
4 +
which is

You can put this solution on YOUR website!
2yds=6ft
6/16=3/8ft

You are to rationalize the denominator

To do that we make the denominator into a perfect square:

To become a square the 3 in the bottom needs to be multiplied by 3
To become a square the x³ in the bottom needs to be multiplied by x
To become a square the y in the bottom needs to be multiplied by y

So we multiply under the radical by the unit fraction  

 =  =  = 

Edwin