Radical/root problems -- multiple choice questions

I'm utterly lost. Please help. How do I do this?

Assuming x and y are positive real numbers, simplify the following expression completely: √20x^8y^13
a) 2x^4y^6√5y
b) x^4√20y^13
c) x^4y^6√20y
d) 2x^4y^6√5x^4y^7



Solve -5+8√x-4=10 for x.
a) 481/64
b) √15/8 + 4
c) 136/9



Multiply and then simplify completely: (2√1+4√6) (2√7-4√6)
a) 4√7 - 16√6
b) -12√1
c) -68

√20x^8y^13

is the same as

√4 times √5 times x^(8/2) times √y^13

2 times √5 times x^4 times √y^13

2x^4 √5y^13

BUT we can split the y^13 into y^12 and y^1:

2x^4 (√5 times √y^12 times √y^1)

2x^4 (√5 times y^(12/2) times √y)

2x^4 (√5 times y^6 times √y)

2x^4y^6 √5y

cant simplify further, OPTION A







assuming equation is

-5 + 8(√(x-4)) = 10

8(√(x-4)) = 10 + 5

8(√(x-4))/8 = 15/8

√(x-4) = 15/8

(√(x-4))^2 = (15/8)^2

x - 4 = 225/64

x = 4 + 225/64

x = 256/64 + 225/64

x = 481/64

can't simplify further, OPTION A









(2√1 + 4√6)(2√7 - 4√6)

first simplify

[2(1) + 4√6)(2√7 - 4√6)

2(2√7) + 2(-4√6) + 4√6(2√7) + 4√6(-4√6)

4√7 - 8√6 + 8√42 - 16√36

4√7 - 8√6 + 8√42 - 16(6)

4√7 - 8√6 + 8√42 - 96

are you sure you typed this expression in correctly?