Questions: Simplify by taking roots of the numerator and denominator. Assume all variables represent positive numbers. √(4/y^2)

Solution Steps

To simplify the given expression by taking roots of the numerator and denominator, we can separately take the square root of the numerator and the square root of the denominator.

1. Take the square root of the numerator (4).
2. Take the square root of the denominator (\(y^2\)).
3. Simplify the resulting expression.

The numerator of the expression is \(4\). Taking the square root gives us: \[ \sqrt{4} = 2 \]

The denominator of the expression is \(y^2\). Taking the square root gives us: \[ \sqrt{y^2} = y \]

Now, we can combine the results from the previous steps to form the simplified expression: \[ \frac{\sqrt{4}}{\sqrt{y^2}} = \frac{2}{y} \]

Final Answer