# Thread: I need help with denominator ratialization

1. ## I need help with denominator ratialization

Hello

I was wandering can anyone help me with rationalization of denominator in this fraction: | a/sqrt(a * sqrt(a)) |

I tried to solve this like this: I multiply both numerator and denominator with | sqrt(a * sqrt(a)) | to get | a * sqrt(a) | in the denominator. Then I multiplied both numerator and denominator with | sqrt(a) to get | a^2 | in denominator. Please tell me if this is right and if it is not, help

P.S. I have a final solution to this problem (in the book), and it is | sqrt[3](a) | but I can't get to that help please

2. if i'm not mistaking,
$\displaystyle \left | \frac{a}{\sqrt{a\sqrt{a}}} \right |=a^{\frac{1}{4}}$

3. Originally Posted by Raoh
if i'm not mistaking,
$\displaystyle \left | \frac{a}{\sqrt{a\sqrt{a}}} \right |=a^{\frac{1}{4}}$
You are not mistaking, I made a mistake in text.

4. $\displaystyle \left | \frac{a}{\sqrt{a\sqrt{a}}} \right |=\left | \frac{a}{\sqrt{a\sqrt{a}}} \right |\times \left | \frac{\sqrt{a\sqrt{a}}}{\sqrt{a\sqrt{a}}} \right |= \frac{\left | a \right |\sqrt{a\sqrt{a}}}{\left | a \right |\sqrt{a}} =\frac{\sqrt{a^2\sqrt{a}}}{\left | a \right |}=\frac{\left | a \right |\sqrt{\sqrt{a}}}{\left | a \right |}=a^{\frac{1}{4}},a\in \mathbb{R}$

5. I solved it in the meantime by myself but I used a different method... I turned every root in power with rational exponent and then I simply added, subtracted and multiplied exponents depending on the operation. Thanks anyway.