# Square Within Square Root

• Jan 21st 2007, 04:55 AM
symmetry
Square Within Square Root
How do I handle square root within square root questions?

I don't have a sample question, though.

Can anyone help me?
• Jan 21st 2007, 05:10 AM
earboth
Quote:

Originally Posted by symmetry
How do I handle square root within square root questions?

I don't have a sample question, though.

Can anyone help me?

Hello,

consider a root to be a power to a rational exponent. Example:

$\sqrt{\sqrt{a}}=\left( a^{\frac{1}{2}} \right)^\frac{1}{2}=a^{\frac{1}{4}}$

In general:

$\sqrt[x]{\sqrt[y]{a}}=a^{\frac{1}{x} \cdot \frac{1}{y}}=\sqrt[x \cdot y]{a}$

EB
• Jan 21st 2007, 05:12 AM
symmetry
ok
Thank you so much.

I had no idea that such formulas existed.

Now it all makes sense.

Thanks!