simplify. 5 sqrt of 150.?

Question

Simplify. 2 sqrt 12+4 sqrt of 27. The last one is (6+ sqrt 6)*(6- sqrt 6). I really appreicate if someone can help me on these.

Answer 1

5 sqrt of 150
5*sqrt(150)
5*sqrt(3*25*2)
5*5*sqrt(3*2)
25+sqrt(6)


2 sqrt 12+4 sqrt of 27
2sqrt(12)+4sqrt(27)
2sqrt(4*3)+4sqrt(9*3)
2*2*sqrt(3)+4*3*sqrt(3)
4*sqrt(3)+12*sqrt(3)
16sqrt(3)


(6+ sqrt 6)*(6- sqrt 6)
this is of the form (a+b)(a-b)=a^2-b^2,
here a=6 & b=sqrt6

so substutitng we get
(6+ sqrt 6)*(6- sqrt 6)
[(6)^2-(sqrt6)^2]
[(36)-(6)]
[36-6]
30

Answer 2

Question 1
5 √150 = 5√(6 x 25) = 25√6

Question 2
2√12 + 4√27
2√(4 x 3) + 4√(9 x 3)
4√3 + 12√3
16√3

Question 3
(6 + √6)(6 - √6)
36 - 6√6 + 6√6 - 6
30

Answer 3

By factoring 150 you can write the expression as

5sqrt(2x3x5x5) and the sqrt of 5x5 is 5 so the result is

25sqrt(6)

Answer 4

5 sqrt(150) = 5sqrt(25*6) = 5sqrt(25)*sqrt(6) = 25sqrt(6)
2sqrt(12) = 2sqrt(4)*sqrt(3) = 4sqrt(3)
4sqrt(27) = 4sqrt(9)*sqrt(3) = 12sqrt(3)
So, the whole thing is (4+12)sqrt(3)=16sqrt(3)

The last is, using FOIL:
6^2 - 6sqrt(6) + 6sqrt(6) + (sqrt(6))^2
36 + 6 = 42

Answer 5

5√150 =

5√25√6 =

5 x 5 √6 =

25√6

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