What is the following product?

Question

asked Feb 1, 2021 179k views

1 Answer

Danieltahara · Answer 1 · 2021-02-05T09:58:43+0000

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)