Question

What is the following sum in simplest form? square root 8 + 3 square root 2 + square root 32

Answer 1

9
`√(2)`

Explanation:

Using the rule of radicals

`√(a)` ×
`√(b)` ⇔
`√(ab)`

Simplify each radical before summing

`√(8)` =
`√(4(2))` = 2
`√(2)`

3
`√(2)` is in simplified form

`√(32)` =
`√(16(2))` = 4
`√(2)`

Hence

2
`√(2)` + 3
`√(2)` + 4
`√(2)` = 9
`√(2)`