Simplify ( square root of 5y^2)^2

${(\sqrt{5} y^{2})}^{2}$

Apply the product rule to $\sqrt{5} y^{2}$ .

${\sqrt{5}}^{2} {(y^{2})}^{2}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

${(5^{\frac{1}{2}})}^{2} {(y^{2})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$5^{\frac{1}{2} \cdot 2} {(y^{2})}^{2}$

Combine $\frac{1}{2}$ and $2$ .

$5^{\frac{2}{2}} {(y^{2})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$5^{\frac{2}{2}} {(y^{2})}^{2}$

Rewrite the expression.

$5^{1} {(y^{2})}^{2}$

Evaluate the exponent.

$5 {(y^{2})}^{2}$

Multiply the exponents in ${(y^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$5 y^{2 \cdot 2}$

Multiply $2$ by $2$ .

$5 y^{4}$