How do you simplify #4sqrt27-sqrt75#?

1 Answer
Mar 21, 2018

Answer:

#4sqrt27-sqrt75=color(blue)(12sqrt3-5sqrt5#

Explanation:

Simplify:

#4sqrt27-sqrt75#

Prime factorize #sqrt27#.

#4sqrt(3^2xx3)-sqrt75#

Apply rule: #sqrt(a^2)=a#

#4xx3sqrt3-sqrt75#

Simplify.

#12sqrt3-sqrt75#

Prime factorize #sqrt75#.

#12sqrt3-sqrt(5^2xx5)#

Apply rule: #sqrt(a^2)=a#

#12sqrt3-5sqrt5#

This is as far as we can go. Since the radicands are not the same, we can not add or subtract.