Question

What is the following product?

Answer 1

Answer: A

Step-by-step explanation:

$(\sqrt{12}+\sqrt{6})(\sqrt{6}-\sqrt{10})$

$(\sqrt{12}*\sqrt{6})-(\sqrt{12}* \sqrt{10})+(\sqrt{6}*\sqrt{6})-(\sqrt{6}*\sqrt{10})$

$(\sqrt{12*6})-(\sqrt{12*10})+(\sqrt{6*6})-(\sqrt{6*10})$

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.

$(\sqrt{3*2^2*6})-(\sqrt{3*2^2*10})+(\sqrt{6^2})-(\sqrt{6*10})$

$(2\sqrt{18})-(2\sqrt{30})+(6)-(\sqrt{60})$

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.

$(2\sqrt{2*3^2})-(2\sqrt{30})+(6)-(\sqrt{15*2^2})$

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

$(2*3\sqrt{2})-(2\sqrt{30})+(6)-(2\sqrt{15})$

Solve and eliminate parentheses.

$6\sqrt{2}-2\sqrt{30}+6-2\sqrt{15}$