# How do you simplify -sqrt5*sqrt20?

Jul 14, 2018

$- 10$

#### Explanation:

$\text{using the "color(blue)"laws of radicals}$

•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)

•color(white)(x)sqrtaxxsqrta=a

$- \sqrt{5} \times \sqrt{20}$

$= - 5 \times \sqrt{4 \times 5}$

$= - 5 \times 2 \sqrt{5}$

$= - \sqrt{5} \times \sqrt{5} \times 2 = - 5 \times 2 = - 10$

$\textcolor{red}{\text{OR}}$

$- \sqrt{5} \times \sqrt{20} = - \sqrt{5 \times 20} = - \sqrt{100} = - 10$

Jul 14, 2018

We can use a "shortcut" method, and multiply the numbers inside the radicals to get

$- \sqrt{100}$

This just simplifies to

$- 10$

A more systematic approach would be to see if we can simplify $\sqrt{20}$. $20$ is the same as $4 \cdot 5$, so we can rewrite $\textcolor{b l u e}{\sqrt{20}}$ as

$- \sqrt{5} \cdot \textcolor{b l u e}{\sqrt{4} \cdot \sqrt{5}}$

Since we are just multiplying, we can rewrite this as

$- \sqrt{5} \cdot \sqrt{5} \cdot \sqrt{4}$

This simplifies to

$- 5 \sqrt{4}$

$- 5 \cdot 2 = - 10$

Either way, we get $- 10$.

Hope this helps!