One problem-Algebra 2- Help!

[Shtatic]

Ok, so my teacher assigned us homework and told us to figure out how to find the cube root of the square root of eight.

As you may have determined, I have no clue how to do this. I just need to simplify the equation. I know the answer is square root of 2, I need to know how to get there. This is all I have:

Cube root of the square root of 8
Cube root of 2 square root of 2
?
?
Please help!

 

[Denis]

Cube root of the square root of 8 : [8^(1/2)]^(1/3)
Cube root of 2 square root of 2 : [2^1 * 2^(1/2)]^(1/3)
? = [2^(3/2)]^(1/3)
? = 2^[(3/2)*(1/3)] = 2^(1/2)

 

[Shtatic]

You are BRILLIANT! Thank you so much for your help!

 

[lookagain]

Ok, so my teacher assigned us homework and told us to figure out how to find the cube root of the square root of eight.

As you may have determined, I have no clue how to do this. I just need to simplify the >> equation << .
I know the answer is square root of 2, I need to know how to get there.

Shtatic,

you are simplifying an expression.

Here is an alternative method:

When you take the cube root of the square root of a number, it is the same result as taking the square root
of the cube root of that number.

\(\displaystyle \sqrt[3]{\sqrt{8}} = \sqrt{\sqrt[3]{8}} = \sqrt{2}\)