Question

1. Enter your answer and show all the steps that you use to solve this problem in the space provided.

Simplify
4√6/√30
by rationalizing the denominator. Show your work.

2. Enter your answer and show all the steps that you use to solve this problem in the space provided.

Simplify
(2√5+3√7)^2
. Show your work. Justify each step.

Answer 1

1,

Multiply numerator and denominator by √30

4 ∙ √6 ∙ √30 / √30 ∙ √30 = 4 ∙ √6 ∙ √30 / 30 = 4 ∙ √ ( 6 ∙ 30 ) / 30 =

4 ∙ √180 / 30 = 4 ∙ √ ( 36 ∙ 5 ) / 30 = 4 ∙ √ ( 6² ∙ 5 ) / 30 =

4 ∙ 6 ∙ √ 5 / 30 = 6 ∙ 4 ∙ √ 5 / 6 ∙ 5 = 4 ∙ √ 5 / 5 =

4 ∙ √ 5 / √ 5 ∙ √ 5 = 4 / √ 5

2.

Use square of sum formula:

( a + b )² = a² + 2 ∙ a ∙ b + b²

( 2 √5 + 3 √7 )² = ( 2 √5 )² + 2 ∙ 2 √5 ∙ 3 √7 + ( 3 √7 )² =

2² ∙ (√5 )² + 12 √5 ∙ √7 + 3² ∙ ( √7 )² = 4 ∙ 5 + 12 √ ( 5 ∙ 7 ) + 9 ∙ 7 =

20 + 12 √35 + 63 = 83 + 12 √35

Answer 2

OH MY GOSH THANK YOU SO MUCH!