How do you simplify #3 times sqrt 8 + sqrt 18#?

1 Answer
Feb 7, 2016

Answer:

#3xxsqrt8+sqrt18=9sqrt 2#

Explanation:

#3xxsqrt8+sqrt18#

Factor #sqrt8#.

#sqrt(2xx2xx2)=#

#sqrt(2^2xx2)#

Apply the square root rule #sqrt(a^2)=a#.

#sqrt(2^2xx2)=2sqrt 2#

#sqrt 8=2sqrt 2#

Rewrite the original expression.

#3xx2sqrt2+sqrt18#

Factor #sqrt 18#.

#sqrt(2xx3xx3)=#

#sqrt(2xx3^2)=#

Apply the square root rule #sqrt(a^2)=a#.

#sqrt(2xx3^2)=3sqrt 2#

#sqrt 18=3sqrt 2#

Rewrite the expression.

#3xx2sqrt2+3sqrt2#

Simplify and add both terms.

#6sqrt 2+3sqrt2=#

#9sqrt 2#