Question

What is the simplified form of the following expression? 2 Sqrt 18+3 Sqrt 2 + Sqrt 162

Answer 1

18√2

Explanation:

2√18 + 3√2 + √162

= 2√(9 * 2) + 3√2 + √(81 * 2)

= (2 * 3)√2 + 3√2 + 9√2

= 6√2 + 3√2 + 9√2

= (6 + 3 + 9)√2

= 18√2

Answer 2

Simplified form is
`√(2)( 18)`.

Explanation:

Given : 2 Sqrt 18+3 Sqrt 2 + Sqrt 162.

To find : What is the simplified form.

Solution : We have given
`2√(18) + 3√(2) +√(162)`.

We can write 18 as 9 *2 and 162 as 81 *2.

`2√(9 * 2) + 3√(2) +√(81 * 2)`.

By radical rule :
`√(a * b) = √(a) * √(b)`

`2 * 3√( 2) + 3√(2) +9\ √(2)`.

`6√( 2) + 3√(2) +9\ √(2)`.

Taking common
`√(2)` from each term

`√(2)( 6 +3 + 9)`.

`√(2)( 18)`.

Therefore, Simplified form is
`√(2)( 18)`.