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

(√12+√6)(√6-√10)
= √12 √6 - √12 √10 +√6 √6  - √6√10
= √72 - √120 + 6 - √60
= 6√2 - 2√30 + 6 - 2√15

Answer is A
6√2 - 2√30 + 6 - 2√15

Answer 2

ANSWER

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

EXPLANATION

We want to find the product

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

We apply the distributive property to get,


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



We expand to obtain,

$\sqrt{12} \times \sqrt{6} - \sqrt{12} \times \sqrt{10} + \sqrt{6} \times \sqrt{6} - \sqrt{6} \times \sqrt{10}$


We now simplify to get,


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

The correct answer is option A.