# What is 5 root 2 Squared ?

#### shayodonn

##### New member
Hi,

What's 5 root 2 squared?

#### MarkFL

##### Super Moderator
Staff member
Can you show what you've tried so we can better help?

#### pka

##### Elite Member
What's 5 root 2 squared?
Had you shown some of your own work it could have avoided some confusion.
As written, the question could be read $$\displaystyle (5\sqrt{2})^2$$ OR $$\displaystyle 5(\sqrt2)^2$$. Do you see the difference?
Which is it? Or is it something else altogether?

#### HallsofIvy

##### Elite Member
"Five root 2" is terribly ambiguous. Most people, like pka, would interpret it as "5 times the square root of 2"- and even then "five root 2 squared" is ambiguous as to whether only "root 2" is being squared, $$\displaystyle 5(\sqrt{2})^2= 5(2)= 10$$ or whether the whole "five root 2" is being squared, $$\displaystyle (5\sqrt{2})^2= 25(2)=50$$.

I would go even further and worry that by "five root 2" you actually mean the fifth root of 2, $$\displaystyle \sqrt[5]{2}$$. If that is what is meant, $$\displaystyle \left(\sqrt[5]{2}\right)^2$$ can be written $$\displaystyle \sqrt[5]{2^2}= \sqrt[5]{4}$$ or as $$\displaystyle 2^{\frac{2}{5}}= 4^{\frac{1}{5}}$$.