# How do you simplify (sqrty-5)^2?

Apr 11, 2018

#### Explanation:

I really hope that you know how to foil so I am not going to explain it but once you expand you get $\left(\sqrt{y} - 5\right) \left(\sqrt{y} - 5\right)$. If you did not know when you multiply two roots the cancel and the middle number stays the same. So when you foil you should get $y - 5 \sqrt{y} - 5 \sqrt{y} + 25$ which simplifies to $y - 10 \sqrt{y} + 25$.

Apr 11, 2018

$y - 10 \sqrt{y} + 25$

#### Explanation:

Using the FOIL method, you can multiply the two terms inside the parenthesis together.

${\left(\sqrt{y} - 5\right)}^{2} = \left(\sqrt{y} - 5\right) \left(\sqrt{y} - 5\right)$

F means "first terms."

$\sqrt{y} \cdot \sqrt{y} = {\sqrt{y}}^{2} = y$

I means "inner terms."

$- 5 \cdot \sqrt{y} = - 5 \sqrt{y}$

O means "outer terms."

$\sqrt{y} \cdot - 5 = - 5 \sqrt{y}$

Finally, L means "last terms."

$- 5 \cdot - 5 = 25$

$y + \left(- 5 \sqrt{y}\right) + \left(- 5 \sqrt{y}\right) + 25$
$= y - 10 \sqrt{y} + 25$