Question

Simplify (√12-√6) (√6+√3).

A) 2√3
B) 2√3 + 12
C) 2√3 - 12
D) √54

Answer 1

Alright. So let's start out with expanding the whole thing. Could you do that? :)

Answer 2

Like, √12 • √6 + √12 • √3 - √6 • √6 - √6 •√3 ?

Answer 3

Yup :)

Answer 4

Then we can simplify from there.

Answer 5

Oh.. I know that the part with √6 •√6 equals 6, so it would be √12 •√6 + √12 • √3 - 6 - √6 • √3 , but I don't know where to go from there...

Answer 6

Alright. What's 12 x 6?
Similarly, what 12 x 3 and 6 x 3?

Answer 7

12 x 6 = 72
12 x 3 = 36
6 x 3 = 18

So would it be √72 - √18 ?

Answer 8

Nice!
Alright.
Do you know how to simplify square root 72 and square root 18?
Like 18 would be 3 square root 2?

Answer 9

Yeah, I think... So √72 would be 6√2 and, like you said, √18 wold be 3√2?

Answer 10

it will be like... √72 - √18... = 6√ 2 - 3√2...

Answer 11

Nice. :D
Now you have like terms, and you can subtract. :)

Answer 12

Thank you @anitasonia98 ! You're rad!

Answer 13

Ah, thanks! :D

Answer 14

btw, when multiplying square roots, instead of doing the multiplication it's often easier to write down factors and look for *pairs*
thus
√12 •√6 + √12 • √3 - 6 - √6 • √3
becomes
√2 √6 √6 + √4 √3 √3 - 6 - √2 √3 √3
and
6 √2 + 2*3 - 6 -3 √2