Question

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

Answer 1

`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)`