Simplify $-5\sqrt{40}$

Question

How do you do this?

Is it first simplifying $\sqrt{40}.$ If I do that I get $-5\sqrt 4\sqrt{10}$

Which gives me $-10\sqrt{10}.$

I don't think I am correct.

Answer 1

You are correct!

$-5\sqrt{40} = -5\sqrt{4\cdot 10}=-5\cdot\sqrt{2^2\cdot 10}=-5\cdot 2\cdot\sqrt{10}=-10\sqrt{10}$

Answer 2

You are correct. This is because of $(a\cdot b)^n=a^n\cdot b^n$. So, You have $-5\cdot (40)^{\frac{1}{2}}=-5\cdot (4\cdot10)^{\frac{1}{2}}=-5\cdot (4)^{\frac{1}{2}}\cdot(10)^{\frac{1}{2}}=-10\cdot 10^{\frac{1}{2}}=-10^{\frac{3}{2}}$

Answer 3

Nope, you're exactly right. $-10 \sqrt{10}$ is correct.

$\sqrt {40} = \sqrt {4} \times \sqrt{10}$, and as $\sqrt{4} = 2$, then everything else snaps into place once you multiply by $-5$ and attach the surd.