Simplify (4 square root of 2- square root of 98)^2

${(4 \sqrt{2} - \sqrt{98})}^{2}$

Step 1

Simplify each term.

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

${(4 \sqrt{2} - \sqrt{49 (2)})}^{2}$

Rewrite $49$ as $7^{2}$ .

${(4 \sqrt{2} - \sqrt{7^{2} \cdot 2})}^{2}$

Pull terms out from under the radical.

${(4 \sqrt{2} - (7 \sqrt{2}))}^{2}$

Multiply $7$ by $- 1$ .

${(4 \sqrt{2} - 7 \sqrt{2})}^{2}$

Step 2

Simplify terms.

Subtract $7 \sqrt{2}$ from $4 \sqrt{2}$ .

${(- 3 \sqrt{2})}^{2}$

Simplify the expression.

Apply the product rule to $- 3 \sqrt{2}$ .

${(- 3)}^{2} {\sqrt{2}}^{2}$

Raise $- 3$ to the power of $2$ .

$9 {\sqrt{2}}^{2}$

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

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

$9 {(2^{\frac{1}{2}})}^{2}$

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

$9 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$9 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$9 \cdot 2^{1}$

Evaluate the exponent.

$9 \cdot 2$

Multiply $9$ by $2$ .

$18$