When plugging in the area of a circle formula, I ran into something I can't figure out.

Lets say that the radius is (5 sqr root of 2/2) Its a fraction. When plugging it into the formula, it becomes (5 sqr root of 2/2)^2. I know the correct answer is 25/2, however, that is what I am not understanding.

Please clarify for me: Pretending that it is not in fraction form, 5 sqr root of 2 * 5 sqr root of 2 would equal 50, correct?

It becomes 25 * 2= 50, correct?

If you think about this as (5 squared) times ((sq. root of 2) squared) and then all divided by (2 squared) and did each piece separately you would get 25 times 2 or (50) and that would be divided by 4 and you would end up with 25/2.

Originally Posted by KingNathan
When plugging in the area of a circle formula, I ran into something I can't figure out.

Lets say that the radius is (5 sqr root of 2/2) Its a fraction. When plugging it into the formula, it becomes (5 sqr root of 2/2)^2. I know the correct answer is 25/2, however, that is what I am not understanding.

Please clarify for me: Pretending that it is not in fraction form, 5 sqr root of 2 * 5 sqr root of 2 would equal 50, correct?

It becomes 25 * 2= 50, correct?
\displaystyle \begin{align*}\left(\frac{5\sqrt{2}}{2}\right)^2 &= \frac{5^2 (\sqrt{2})^2}{2^2} \\ &= \frac{25\cdot 2}{4} \\ &= \frac{25}{2} \end{align*}