math helpp..5

Question

simplify a) 3√175 + 6√63     b) 6√80 - 2√20

Answer 1

a) The radical expression 3√175 + 6√63

= 3√(25*7) + 6√(9*7)

{ Apply the radical property √ab = √a√b }

= 3√25√7) + 6√9√7

= 3√(5²)√7) + 6√(3²)√7

{ Apply the radical property √(a²) = a where a≥ 0 }

= (3*5)√7 + (6*3)√7

= 15√7 + 18√7

= 33√7

3√175 + 6√63 = 33√7.

Answer 2

b) The radical expression 6√80 - 2√20

= 6√(16*5) - 2√(4*5)

{ Apply the radical property √ab = √a√b }

= 6√16√5) - 2√4√5

= 6√(4²)√5 - 2√(2²)√5

{ Apply the radical property √(a²) = a where a≥ 0 }

= 6(4)√5 - 2(2)√5

= 24√5 - 4√5

= 20√5

6√80 - 2√20 = 20√5.