How do you find get rid of the denominator when it is a cube root of something?

Question

1/(cube root of 2)
How would you simplify it so that there are no roots at the denominator?

Answer 1

multiply top and bottom by 2 squared or 4.

The cube root of any number multiplied by the square of that number is equal to the number itself so...

1/cube root of 2 x 4/4 = 4/2 = 2

Answer 2

You can't cube both the numerator and the denominator, because that'd be like saying 1/2 is equal to 1/8, which it isn't.

So to simplify it, you have to multiply the numerator and the denominator by the same number. So you just have to figure out what number will get rid of the cube root in the denominator, and multiply both the numerator and the denominator by that number.

For cube roots, you would cube the denominator (multiply it by itself twice), so in this case you're multiplying by (cube root 2)(cube root 2), which is the same as cube root 4.

When you multiply the numerator and denominator, you'll get (cube root 4)/2.

Hope this helped!

EDIT: I'm really not sure what everybody else is doing... the closest anybody else got was multiplying the numerator and denominator by cube root 2, because if it were just plain root 2, you would only have to multiply once. But to simplify cube roots, you have to cube, not square.

Answer 3

It is called 'rationalizing the denominator' to do this:
Write the expression as the quotient of radicals.
That is, the cube root of (1/2).
Then multiply both numerator and denominator by the right number of factors of 2 to make the denominator a perfect cube.
Multiply by the cube root of 2squared. This will give you (since 1 is your numerator) the cube root of 2squared over 2.

Answer 4

Easy peasy just cube (^3) the numerator (top) and the denominator (bottom).

You just want to cancel off the bottom to get the 2, and you have to do it on the top and bottom to be fair.

i.e. 1 / cubeROOT2
= ...1^3/ (cuberoot 2)^3
= 1/2

Answer 5

1/(cube root of 2)
Just multiply the numerator and the denominator by cuberoot(2).
This gives cuberoot(2)/2

Answer 6

Cube both sides of the equation. That makes the expression 1/2.

Answer 7

Here is the rule: Bring the denominator into the numerator and change its sign. Therefore 1/(cuberoot of 2) = - cuberoot of 2

Answer 8

cube top and bottom = 1/2