what is (8+squareroot 12)(3- squareroot12)?

Question

* (3+ squareroot3)(3+squareroot2)

* (squareroot100 - 6)(-4 + squareroot 12)

* 4 squarteroot2(squareroot 12 - 3 sqrt 2 + 4 sqrt 8)

Answer 1

= (8 x 3)+(-8 x sq rt12)+(sq rt12 x 3)+(sq rt12 x -(sq rt12))
=24-8sq rt12+3sq rt12+sq rt12-sq rt12
24-5sq rt12


=(3 x 3)+(3sq rt12)+(3sq rt12)+(sq rt12 x sq rt12)
=9 + 6sq rt12 + (12)
= 21+6sq rt12


the next one is a little easier because sq rt100directly = 10
If the teacher lets you use this at the beginning of the solution, then
(10-6)(-4+sq rt12)
=4(-4+sq rt12)
= -16 + 4sq rt12

the last one is direct multiplication of the first number x each of the numbers inside the parentheses using a minus for the middle one.
You can do this now.

Answer 2

I'm assuming that EVERYTHING you've written is one big messy equation, since each line begins with a multiplication symbol connecting it to, and continuing it from, the one before. If it's not, you need to learn the value of proper punctuation.

Start: (8+√12)(3−√12)(3+√3)(3+√2)(√100−6)(−4+√12)(4√2[√12−3√2+4√8])

Let's redefine the last, (4√2[√12−3√2+4√8]) as follows:
4×√2×√12 = 4×√24 = 4×√4×√6 = 4×2×√6 = 8×√6, and
4×√2×(−3)×√2 = −3×4×2 = −24, and
4×√2×4×√8 = 4×4×√16 = 4×4×4 = 64.
Thus (4√2[√12−3√2+4√8]) = 64 − 24 + 8√6 = 40 + 8√6.

And the 3rd-to-last, (√100−6), is just 10 − 6 = 4.

Combining those two, 4 × (40+8√6) = 160 + 32√6.

Rewrite the whole equation now as
(8+√12)(3−√12)(3+√3)(3+√2)(−4+√12)(160+32√6).

Combine the first two terms as
(24 − 8√12 −3√12 +12) = 36−11√12.

Rewrite the whole equation now as
(36−11√12)(3+√3)(3+√2)(−4+√12)(160+32√6).

Combine two terms (36−11√12)(−4+√12)=(−276+80√12).

Rewrite the whole equation now as
(−276+80√12)(3+√3)(3+√2)(160+32√6).

Combine the middle two terms.
(3+√3)(3+√2) = (9 + 3√2 + 3√3 + √6).

Our equation is now (−276+80√12)(9+3√2+3√3+√6)(160+32√6).

Middle & last terms. (9+3√2+3√3+√6)(160+32√6) =
(1632+448√6+480√2+480√3+96√12+96√18).
That didn't help much.

Still, now we have
(−276+80√12)×(1632+448√6+480√2+480√3+96√12+96√18).

And that gives
−127872 + 3072√2 +75648√3 − 768√6 +75648√3 ≈ 5617.435432
assuming I've made no mistakes, which is doubtful. (Note that √18 = 3√2 and √12 = 2√3, which I should have used a couple of steps ago.)