Simplify √15(-2√5 + 4√6) ? (10 points guaranteed for the help)

I think the square root over the 15 is over the whole equation (i think).

ANSWER: -10√3 + 12√10

I don't know how they got the answer. Can someone please show me the answer?

1√15(-2√5 + 4√6)

1√15(-2√5) + 1√15(4√6)

(1)(-2)(√(15x5)) + 1(4)(√(15x6))

-2√75 + 4√90

-2(√(25x3)) + 4(√(9x10))

-2(√25 x √3) + 4(√9 x √10)

-2(5√3) + 4(3√10)

-10√3 + 12√10

can't simplify further

√15(-2√5 + 4√6)
multiply the √15 into both sets
√15*(-2√5) + √15*(4√6)
whenever dealing with square roots, you can break it up. for example... √15 can be broken up into √5*√3, if you're dealing with something like √20, you want to think of factors (1,2,4,5,10,20) and find what combination of them would create 20, along with creating an integer, rather than just a square root of something. Since you know √4 is the only one there that can have a perfect square root taken, you want to include that and something else that multiplies to 20, in this case 5. so √20 could be re-written as √4*√5, or 2√5

knowing this, split √15*(-2√5) + √15*(4√6)
first portion=>√5*√3*-2*√5 since this has √5 and √5 being multiplied together, you may say that (√5)^2 = 5, and 5*-2 = -10, that is being multiplied by √3, so the first part, that's how they get -10√3

second portion=> √5*√3*4*√3*√2 since there are √3 and √3 being multiplied, treat it as being squared, and (√3)^2 = 3, and 3*4 = 12. When multiplying square roots, you can do it just like integers, just make sure to include the square root, so √5*√2 = √10, and √10*12 = 12√10

now add the first portion ( -10√3 ) and the second portion (12√10)
and you will get -10√3 + 12√10

Hope this helped :)

-2√75+4√90
-2(5√3)+4(3√10)
-10√3+12√10

√15*√5=√75 which then equals √25*3= 5√3
√15*√6=√90 which then equals √9*10= 3√10

=-2√75 + 4√90 = -10√3 + 12√10