Question

simplify.
\sqrt{25y^{6}}
assume that the variable y represents a pos

Explanation:

Step1: Simplify the coefficient

We know that $\sqrt{25} = 5$ because $5\times5 = 25$.

Step2: Simplify the variable term

For the variable part $y^{6}$, using the property of square roots $\sqrt{x^{n}}=x^{\frac{n}{2}}$ (when $x\geq0$), so $\sqrt{y^{6}}=y^{\frac{6}{2}} = y^{3}$.

Step3: Combine the results

Multiply the simplified coefficient and the simplified variable term together. So $\sqrt{25y^{6}}=\sqrt{25}\times\sqrt{y^{6}} = 5\times y^{3}=5y^{3}$.

Answer:

$5y^{3}$