simplify the following?

Question

2 sq root 12 + 4 sq root 20 - 3 sq root 27 - 5 sq root 45

and

(2 sq root 3 - 3 sq root 2) (sq root 5 + 4 sq root 45)

Answer 1

Question 1
2.√12 + 4.√20 - 3.√27 - 5.√45
4.√3 + 8.√5 - 9.√3 - 15.√5
- 5.√3 - 7.√5

Question 2
(2.√3 - 3.√2).(√5 + 12.√5)
2 √15 + 24.√15 - 3.√10 - 36. √10
26.√15 - 39.√10

Answer 2

Anything under a square root that can be factored into something square should be. For example, 12 = 4 * 3, so sqrt 12 is sqrt 4 * sqrt 3. Sqrt 4 is 2, so sqrt 12 is actually 2 * sqrt 3.

12 = 4 * 3
20 = 4 * 5
27 = 9 * 3
45 = 9 * 5

2 sqrt 12 = 2 * 2 sqrt 3
4 sqrt 20 = 4 * 2 sqrt 5
3 sqrt 27 = 3 * 3 sqrt 3
5 sqrt 45 = 5 * 3 sqrt 5

4 sqrt 3 - 9 sqrt 3 + 8 sqrt 5 - 15 sqrt 5 =
-5 sqrt 3 - 7 sqrt 5

The second one needs to be FOILed and done the same way to simplify.

Answer 3

2 sq root 12 + 4 sq root 20 - 3 sq root 27 - 5 sq root 45
= 2*2sqrt(3)+4*2sqrt(5)-3*3sqrt(3)-5*3sqrt(5)
=4sqrt3+8sqrt5-9sqrt3-15sqrt5
- that's for the 1st one

the second one..you have to foil it

this is the easiest way to factor and simplify: a factoring tree
consult this site: http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html

I have to leave, but I hope this helped!

Answer 4

6 sqrt 3 - 9 sqrt3 - 15 sqrt 5
-3sqrt3 - 15sqrt5

and

(2sqrt3 - 3sqrt2)(sqrt5 + 12sqrt5)
(2sqrt3 - 3sqrt2)(13sqrt5)
26sqrt15 - 39sqrt10