Question

Simplify. All variables represent nonnegative numbers.

sqrt(x^4,y^2)

Answer 1

`\displaystyle{√(x^4y^2) = x^2y}`

Explanation:

We can expand into multiplication:

`\displaystyle{√(x^4 y^2) = √(x \cdot x \cdot x \cdot x \cdot y \cdot y)}`

Since it's radical, we take off two terms and make it as one outside. There are four x's; take two x's and make them one. There are two y's; take two out and make them one. Therefore:

`\displaystyle{√(x \cdot x \cdot x \cdot x \cdot y \cdot y ) = x\cdot x \cdot y}`

Simplify further, therefore:

`\displaystyle{√(x \cdot x \cdot x \cdot x \cdot y \cdot y ) =x^2y}`

Hence:

`\displaystyle{√(x^4y^2) = x^2y}`