Which expression is equivalent to sqrt(x+y^2)

Question

A.x 1/2 +y

b. (Xy^2)^1/2

c. (X^2+y^4)^1/2

d. (X+y^2)^1/2

Answer 1

sqr(x+y^2) = (x+y^2)^1/2

the square root is the same as an exponent = 1/2

the root and the exponent are inverses

a cube root is the same as an exponent = 1/3

4th root equivalent to an exponent of 1/4

Another equivalent expression would be

the square of the 4th root

[4th root (x+y^2)]^2

or

also equivalent

the 8th root raised to the 4th power

[8th root (x+y^2)]^4

Answer 2

if simplifying a square root, you normally would have a factor in common with the whole expression.( x + y^2), does not seem to have a clear way to be factored. However, if the expression inside the square root is (x+y)^2, then it would work. the square root of any squared number, such as 2^2, is just the expression being squared. In our case that is x+y.