Question

What is the following product? ( sqrt 12+ sqrt 6)(sqrt 6- sqrt 10)

Answer 1

Option A.

Explanation:

The given expression is

`(√(12)+√(6))(√(6)-√(10))`

We need to find the product.

Using distributive property we get

`√(12)(√(6)-√(10))+√(6)(√(6)-√(10))`

`√(12)(√(6))+√(12)(-√(10))+√(6)(√(6))+√(6)(-√(10))`

Using the properties of radical expressions we get

`√(12\cdot 6)-√(12\cdot 10)+√(6\cdot 6)-√(6\cdot 10)`
`[\because \sqrt a\sqrt b=√(ab)]`

`√(72)-√(120)+√(36)-√(60)`

On further simplification we get

`6√(2)-2√(30)+6-2√(15)`

Therefore, the correct option is A.