help please !!

Question

MULTIPLY AND EXPRESS EACH ANSWER IN SIMPLEST FORM.

1.)   √5(√8)

2.) (5+√3)(7-√3)

3.) 4x√12(3x²√6)

Answer 1

1)

The radical expression is √5(√8)

{Apply the radical property √(ab) = √a √b where a ≥ 0 and b ≥ 0}

= √5√(2*4)

= √5√2√4

= 2√5√2

= 2√(5*2)

√5(√8) = 2√10.

Answer 2

2) The radical expression is (5 + √3)(7 - √3)

= 5(7) + 5(-√3) + (√3)(7) + (√3)(-√3)

{Apply the property √a (√a) = a}

= 35 - 5√3 + 7√3 - 3

(5 + √3)(7 - √3) = 32 + 2√3.

Answer 3

3)

The radical expression is 4x√12(3x²√6)

{Apply the radical property √(ab) = √a √b where a ≥ 0 and b ≥ 0}

= 4x√(4*3)[3x²√(3*2)]

= 4x√4√3[3x²√3√2]

 = 4x(2)√3[3x²√3√2]

= 24x³√3√3√2

{Apply the property √a (√a) = a}

= 24x³(3)√2

= 72x³√2

4x√12(3x²√6) = 72x³√2.