Question

What is the following product?

Answer 1

Answer: A

Explanation:

`(√(12)+√(6))(√(6)-√(10))`

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

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

Let's rewrite the numbers inside to see if we can take some out.

For example; 12 is 3 x 4 and 4 is
`2^2` which means a 2 will come out of the root.

`(√(3*2^2*6))-(√(3*2^2*10))+(√(6^2))-(√(6*10))`

`(2√(18))-(2√(30))+(6)-(√(60))`

We can also rewrite 18 as 9 x 2 and 9 can be rewritten as
`3^2` which will make the 3 come out.

60 can be rewritten as 15 x 4 and 4 can be rewritten as
`2^2` which will make the 2 come out.

Let's rewrite this.

`(2√(2*3^2))-(2√(30))+(6)-(√(15*2^2))`

When a number comes out of a root, it has to be multiplied by the number that is already outside.

`(2*3√(2))-(2√(30))+(6)-(2√(15))`

Solve and eliminate parentheses.

`6√(2)-2√(30)+6-2√(15)`