Question: Simplify. \(\sqrt{25y^{10}}\) Assume that the variable \(y\) represents a positive real…

Simplify.

\(\sqrt{25y^{10}}\)

Assume that the variable \(y\) represents a positive real number.

Solution

To simplify the expression \(\sqrt{25y^{10}}\), follow these steps: Identify the square root components: \[ \sqrt{25y^{10}} = \sqrt{25} \cdot \sqrt{y^{10}} \] Calculate the square root of 25, which is 5: \[ \sqrt{25} = 5 \] Simplify \(\sqrt{y^{10}}\) by expressing \(y^{10}\) as \((y^5)^2\): \[ \sqrt{y^{10}} = \sqrt{(y^5)^2} = y^5 \] Combine the results: \[ \sqrt{25y^{10}} = 5 \cdot y^5 = 5y^5 \] The simplified expression is \(5y^5\).