Evaluate (5 square root of 2)^2

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

Step 1

Simplify the expression.

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

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

Raise $5$ to the power of $2$ .

$25 {\sqrt{2}}^{2}$

Step 2

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

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

$25 {(2^{\frac{1}{2}})}^{2}$

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

$25 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$25 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$25 \cdot 2^{1}$

Evaluate the exponent.

$25 \cdot 2$

Step 3

Multiply $25$ by $2$ .

$50$