Question

what is the following product? (√12+√6)(√6-√10)
A) 6√2-2√30+6-2√15
B) 6√3-6√5
C) 3√2-√22+2√3-4
D) 2√3+6-2√15

Answer 1

Answer is A, (√12+√6)(√6-√10)

Answer 2

Answer:

The correct option is A.

Step-by-step explanation:

The given expression is

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

Using distributive property of multiplication, we get

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

Using distributive property of multiplication, we get

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

$\sqrt{72}-\sqrt{120}+\sqrt{36}-\sqrt{60}$

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

The simplified form of the given expression is $6\sqrt{2}-2\sqrt{30}+6-2\sqrt{15}$. Therefore the correct option is A.