Question

Match each expression with its equivalent expression.

a. √4x^2y^4
b. √8x^2y
c. √4x^2y
c. √16xy^2
d. √8xy^2

1. 2x√y
2. 2y√2x
3. 2xy^2
4. 2x√2y
5. 4y√x

Answer 1

a -> 3

b -> 4

c -> 1

d -> 5

e -> 2

Explanation:

We apply the properties to solve this question.

a. √4x^2y^4

`√(4x^2y^4) = √(4)√(x^2)√(y^4) = 2xy^2`

So a -> 3

b. √8x^2y

`√(8x^2y) = √(8)√(x^2)√(y) = √(4*2)x√(y) = √(4)√(2)x√(y) = 2x√(2)√(y) = 2x√(2y)`

So b -> 4

c. √4x^2y

`√(4x^2y) = √(4)√(x^2)√(y) = 2x√(y)`

So c -> 1

d. √16xy^2

`√(16xy^2) = √(16)√(x)√(y^2) = 4√(x)y = 4y√(x)`

So d -> 5

e. √8xy^2

`√(8xy^2) = √(8)√(x)√(y^2) = √(4*2)√(x)y = √(4)√(2)√(x)y = 2y√(2)√(x) = 2y√(2x)`

So e -> 2