How do you simplify -sqrt5*sqrt20?

2 Answers
Jim G.
Jul 14, 2018

-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

Jacobi J.
Jul 14, 2018

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!

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