pre calculus question

Question

simplify each of the following expression. show work

a. 7√2 - √32 + 2√128 

b. 6√27 + 5√(48x) - 3√(75x)

 

Answer 1

a)

The radical expression is 7√2 - √32 + 2√128

= 7√2 - √(16*2) + 2√(64*2)

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

= 7√2 - (√16√2) + 2(√64√2)

= 7√2 - 4√2 + 2(8√2)

= 7√2 - 4√2 + 16√2

= 19√2

7√2 - √32 + 2√128 = 19√2.

Answer 2

b)

The radical expression is 6√27 + 5√(48x) - 3√(75x)

= 6√(9*3) + 5√(16*3x) - 3√(25*3x)

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

= 6(√9√3) + 5 [√16√(3x)] - 3[√25√(3x)]

= 6(3√3) + 5 (4√(3x) - 3(5√(3x)

= 18√3 + 20√(3x) - 15√(3x)

= 18√3 + 5√(3x)

= 18√3 + 5√3√x

= √3(18 + 5√x)

6√27 + 5√(48x) - 3√(75x) = √3(18 + 5√x).