square root: how would one simplify 4 root 2, squared?

[navi99]

how do you do something like 4 root 2, squared
would the answer for that be 8 or 32? i used my calculator and when i dont use parenthesis its 8, and when i do use parenthesis its 32

 

[skeeter]

\(\displaystyle \L (4\sqrt{2})^2 = 4^2 \cdot (\sqrt{2})^2 = 16 \cdot 2 = 32\)

 

[stapel]

how do you do something like 4 root 2, squared
would the answer for that be 8 or 32? i used my calculator and when i dont use parenthesis its 8, and when i do use parenthesis its 32

When you use different formatting, you're saying different things, so naturally you would get different answers. Unfortunately, we have no way of knowing (since you didn't show your work) where you might be putting parentheses, nor how the exercise was formatted originally.

Do you mean any of the following?

. . . . .\(\displaystyle \L \sqrt[4]{2^2\,}\)

. . . . .\(\displaystyle \L \left(\sqrt[4]{2\,}\right)^2\)

. . . . .\(\displaystyle \L 4\, \sqrt{2^2\,}\)

. . . . .\(\displaystyle \L \left(\, 4\, sqrt{2\,}\, \right)^2\)

Or do you mean something else?

Thank you.

Eliz.

 

[navi99]

\(\displaystyle \L (4\sqrt{2})^2 = 4^2 \cdot (\sqrt{2})^2 = 16 \cdot 2 = 32\)

^this answered my question, thanks Skeeter and Stapel!!