9th grade Algebra.Square roots. I don't understand. Best answer gets 10 points!

√ 24
√ 4 x 6
2 √ 6

(3 + √ 7) (3 + √ 7) = 9 + 6√7 + 7 = 16 + 6√7

√ (15 √ 3 - 6 √ 6)
3i √ 10
I dunno about the last one. use this : http://mathway.com/problem.aspx?p=algebr…
oh for the last one, that was unnecessary spacing... didnt realize it was rad. 3 I thought it was rad. of whatever 3 distributes and gets.

prob 1)
you are allowed to multiply things that are under the radical sign
√3 x √ 8 = √24 = √4 x √ 6 = 2√6

prob 2
FOIL it out
(3 + √7)(3 + √7) = 9 + 3√7 + 3√7 + 7 = 16 + 6√7

prob 3
distribute the √3 through the parentheses
√3(5√3 - 2√6) = 5√9 - 2 √18 = 5(3) - 2(3)√2 = 15 - 6√2

Multiply the numbers inside the radical sign: √3 x √8 = √(3 x 8) = √24 = √(4 x 6) = √4 x √ 6 = 2√6

(3 + √7)^2: FOIL just like you would do with any other binomial: 9 + 6√7 + 7 = 16 + 6√7

√3(5√3 - 2√6): Distribute √3:
(5√3 x √3) - (2√6 x √3)
5√9 - 2√18; √9 = 3, √18 = 3√2
(5 x 3) - (2 x 3√2)
15 - 6√2

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➊ √ ̅3̅ ̅ √ ̅8̅ = √ ̅3̅·̅8̅ ̅ = √ ̅2̅4̅ ̅            ← used the rule √ ̅a̅ √ ̅b̅ = √ ̅a̅b̅
                               = √ ̅4̅·̅6̅
                               = √ ̅4̅ ̅ √ ̅6̅
                               = 2√ ̅6̅


➋    (3+√ ̅7̅  )²                       ← this is like (a+b)²
    = 3² + 2·3√ ̅7̅  + (√ ̅7̅  )²            ← used rule (a+b)² = a²+2ab+b²
    = 9 + 6√ ̅7̅  + 7            ← used rule (√ ̅a̅ )² = a
    = 16 + 6√ ̅7̅  


➌   √ ̅3̅ (5√ ̅3̅ - 2√ ̅6̅   )                       ← this is like  a(b+c)