Question

How do you simplify `-sqrt5*sqrt20`?

Answer 1

`-10`

Explanation:

`"using the "color(blue)"laws of radicals"`

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

`•color(white)(x)sqrtaxxsqrta=a`

`-sqrt5xxsqrt20`

`=-5xxsqrt(4xx5)`

`=-5xx2sqrt5`

`=-sqrt5xxsqrt5xx2=-5xx2=-10`

`color(red)"OR"`

`-sqrt5xxsqrt20=-sqrt(5xx20)=-sqrt100=-10`

Answer 2

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

`-sqrt100`

This just simplifies to

`-10`

A more systematic approach would be to see if we can simplify `sqrt20`. `20` is the same as `4*5`, so we can rewrite `color(blue)(sqrt20)` as

`-sqrt5*color(blue)(sqrt4*sqrt5)`

Since we are just multiplying, we can rewrite this as

`-sqrt5*sqrt5*sqrt4`

This simplifies to

`-5sqrt4`

`-5*2=-10`

Either way, we get `-10`.

Hope this helps!