Simplify (4 square root of 5)^2

${(4 \sqrt{5})}^{2}$

Step 1

Simplify the expression.

Apply the product rule to $4 \sqrt{5}$ .

$4^{2} {\sqrt{5}}^{2}$

Raise $4$ to the power of $2$ .

$16 {\sqrt{5}}^{2}$

Step 2

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

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

$16 {(5^{\frac{1}{2}})}^{2}$

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

$16 \cdot 5^{\frac{1}{2} \cdot 2}$

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

$16 \cdot 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 \cdot 5^{\frac{2}{2}}$

Rewrite the expression.

$16 \cdot 5^{1}$

Evaluate the exponent.

$16 \cdot 5$

Step 3

Multiply $16$ by $5$ .

$80$