How do you simplify #-sqrt5*sqrt20#?

2 Answers
Jul 14, 2018

Answer:

#-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#

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!