How do you simplify: Square root of 50 + square root of 18?

1 Answer
Jul 12, 2015

Answer:

#8sqrt(2)#

Explanation:

Recall the multiplicative property of square root for positive #a# and #b#:
#sqrt(a*b) = sqrt(a) * sqrt(b)#

Using this rule, we can write
#sqrt(50)=sqrt(25*2)=sqrt(25)*sqrt(2)=5sqrt(2)#

analogously,
#sqrt(18)=sqrt(9*2)=sqrt(9)*sqrt(2)=3sqrt(2)#

Adding them together and using the distributive law, we have
#sqrt(50)+sqrt(18)=5sqrt(2)+3sqrt(2)=8sqrt(2)#