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

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

Step 1

Reorder $5$ and $a^{2}$ .

${\sqrt{a^{2} \cdot 5}}^{2}$

Step 2

Pull terms out from under the radical.

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

Step 3

Apply the product rule to $a \sqrt{5}$ .

$a^{2} {\sqrt{5}}^{2}$

Step 4

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

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

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

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

$a^{2} \cdot 5^{\frac{1}{2} \cdot 2}$

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

$a^{2} \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$a^{2} \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$a^{2} \cdot 5^{1}$

Evaluate the exponent.

$a^{2} \cdot 5$

Step 5

Move $5$ to the left of $a^{2}$ .

$5 a^{2}$