Algebra 2 Homework Help?!! Check if im doing this right

Im stuck on a few problems:
1. f(x)=(square root of x-8) + 7 find all values x fir which f(x)=13

Do i just plug it in? Or do i set it equal to zero?

2. Square root of xy^11(square root of x^7y^3 - square root of x^39y^15)

For the one above i started to distribute the xy^11 and added the powers?

3. (4srt 3 + 15)(4srt 3 -15)
Would it be 12-225= -213? I used the foil method

4.17srt10(8srt2 - 3srt5)
I distributed 17srt10 and got 136srt20 - 51srt50

1. f(x) = sqrt(x-8) + 7, and using f(x) = 13 so
13 = sqrt(x-8) + 7
6 = sqrt(x-8)
36 = x-8
x = 44

2. sqrt(xy^11)*[sqrt(x^7*y^3) - sqrt(x^39*y^15)]
= x^(1/2)*y^(11/2)*[x^(7/2)*y^(3/2) - x^(39/2)*y^(15/2)]
= x^(1/2+7/2)*y(11/2+3/2) - x^(1/2+39/2)*y^(11/2+15/2)
= x^(8/2)*y^(14/2) - x^(40/2)*y^(26/2)
= x^4*y^7 - x^20*y^13

3. yes use foil, im too lazy to write the answer out but your answer is not right. check with your calculator

4. your answer looks right but you can simplify it more
136sqrt(20) = 136*2sqrt(5), etc
51sqrt(50) = 51*5sqrt(2)