Question

(3sqrt(7) -6sqrt(3)) (3sqrt(7) +9sqrt(3)) multiply to solve.

Answer 1

I got -99+9sqrt(21)

Answer 2

1.)
3sqrt(2) * [3 + sqrt(2)]

Distribute for each term:

9sqrt(2) + 3sqrt(2)*sqrt(2) (Multiplying like roots cancels it out to the actual number, 2 in this case)
9sqrt(2) + 3*2
9sqrt(2) + 6

2.)
4 + sqrt(20)/2

Assuming that the 2 is being divided into ONLY the sqrt(20)...

4 + 2sqrt(5)/2 (The 2s cancel here because of division)
4 + sqrt(5)

In the case that the 2 is being divided into BOTH the 4 and the sqrt(2)...

[4 + 2sqrt(5)]/2
2 + sqrt(5)

3.)
12sqrt(18)/3sqrt(2)

Again, simplify the roots as much as possible...
12*3sqrt(2)/3sqrt(2) (The 3sqrt(2) cancels because of division)
12

So, your answers are
1.) 9sqrt(2) + 6
2.) 4 + sqrt(5) (or 2 + sqrt(5), depending)
3.) 12

Answer 3

Wow, great explanation!

Answer 4

\[(3\sqrt{7} -6\sqrt3) (3\sqrt7 +9\sqrt3) = 9*7 + 27\sqrt21 - 18\sqrt21 - 54*3 = 63 + 9\sqrt21 - 162 = -99 + 9\sqrt21\]

Answer 5

or that lol

Answer 6

Thanks

Answer 7

so the answer is 63+9sqrt(21-16)