1/cubed root of 2? I undertsand how i get the denominator but not the top part im still confused?

Question

simplify. one over the cubed root of two. answer is cubed root of four over two. How you get get 2 on the denominator I undertsand but the top i am lost

Answer 1

Write the cube root of 2 as 2^(1/3). You then have :

1/2^(1/3).

What do you need to complete the exponent (i.e., how far away is it from the next whole number) in the denominator? Well, the next whole number is 1, so you are 1 - 1/3 = 2/3 away. So multiply the top and bottom of the fraction by 2^(2/3). We then get:

[1/2^(1/3)] * [2^(2/3)/2^(2/3)] = 2^(2/3) / [2^(1/3) * 2^(2/3)] = 2^(2/3) / 2^(1/3 + 2/3) = 2^(2/3) / 2^1 = 2^(2/3) / 2.

Finally, you can change 2^(2/3) into (2^2)^(1/3) = 4^(1/3) which is the cube root of 4. Or, more generally, whenever you have

a^(m/n),

you can change it into the nth root of a^m.

Answer 2

To rationalize the denominator, you must multiply it by something which will remove the irrational number. For the cube root of 2, you must multiply it by the cube root of 4. Because you do not want to change the value of the fraction, you must also multiply the numerator by the cube root of 4. This effectively multiplies the entire fraction by 1, and so its value is not changed.

In the numerator, 1 times the cube root of 4 equals the cube root of 4.

In the denominator, the cube root of 2 times the cube root of 4 equals the cube root of 8. The cube root of 8 equals 2.

Answer 3

your goal is to get rid of the radical sign in the denominator so you should be looking for the smallest perfect cube with a factor of 2, and that number is 8.

which means you should get a cubed root of 8 in the denominator. to get that, you multiply cubed root of 2 by cubed root of 4. as a rule, whatever you multiply in the denominator (bottom) must also be multiplied in the numerator (top). so u also multiply 1 by cubed root of 4. the bottom part will be simplified as 2 while the top part, which is 1 times cubed root of 4, becomes cubed root of 4.

hence, your final answer is cubed root of 4 over 2.

hope this helps!

Answer 4

Multplying the top and bottom by the cube root of 4 (Multiplying by an equivalent of 1) creates cube root of 8 on the bottom which is essentially 2.

Answer 5

1/[2^(1/3)] as cube root is (^1/3)
[2^(2/3)]/2 multiplying the numerator & denominator by (2^2/3)
[4^(1/3)]/2
approx 0.79 is the ans

Answer 6

1/(cbrt(2))
1/(2^(1/3))

Multiply top and bottom by 2^(2/3)

(2^(2/3))/(2^(1/3) * 2^(2/3))
(cbrt(2^2))/(2^((1/3) + (2/3)))
(cbrt(4))/(2^(3/3))
(cbrt(4))/(2^1)

ANS : (cbrt(4))/2