What is square root of 8 plus square root of 18 minus the square root of 32?

1 Answer
Zor Shekhtman
Jul 20, 2015

#9sqrt(2)#

Explanation:

The main property this problem is based upon is the property of a square root of a product of two positive numbers:
#sqrt(a*b)=sqrt(a)*sqrt(b)#
(for any positive #a# and #b#).
This property is easy to prove directly from the definition of a square root of a positive number.

Using this for the numbers in this problem, we get:

#sqrt(8)+sqrt(18)+sqrt(32)=sqrt(4*2)+sqrt(9*2)+sqrt(16*2)=#
#=sqrt(4)*sqrt(2)+sqrt(9)*sqrt(2)+sqrt(16)*sqrt(2)=#
#2sqrt(2)+3sqrt(2)+4sqrt(2)=9sqrt(2)#

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