Simplify the Radical Expression ( square root of 8)^2

${(\sqrt{8})}^{2}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

Rewrite $4$ as $2^{2}$ .

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

Pull terms out from under the radical.

${(| 2 | \sqrt{2})}^{2}$

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

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

$2^{2} {\sqrt{2}}^{2}$

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

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

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

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

$4 {(2^{\frac{1}{2}})}^{2}$

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

$4 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$4 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$4 \cdot 2^{1}$

Evaluate the exponent.

$4 \cdot 2$

Multiply $4$ by $2$ .

$8$