How do you simplify #sqrt150 + sqrt 40#?

1 Answer
Mar 21, 2018

Answer:

#5sqrt(6)+2sqrt(10)#

Explanation:

#sqrt(150)+sqrt(40)#
#sqrt(25*6)+sqrt(40)# #color(blue)("Find a factor of 150 that is also a perfect square")#
#5sqrt(6)+sqrt(40)# #color(blue)("Since 25 is a perfect square, pull out a 5")#
#5sqrt(6)+sqrt(10*4)# #color(blue)("Find a factor of 40 that is also a perfect square")#
#5sqrt(6)+2sqrt(10)# #color(blue)("Since 4 is a perfect square, pull out a 2")#

A perfect square is a number that can be pulled out of a radical by multiplying a constant together twice #(5*5=25)#.

#sqrt(6)# and #sqrt(10)# can't be simplified since there are no factors of 6 or 10 that are perfect squares.