Write in Standard Form ( square root of -72)^2

${(\sqrt{- 72})}^{2}$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Rewrite $- 72$ as $- 1 (72)$ .

${\sqrt{- 1 (72)}}^{2}$

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

${(\sqrt{- 1} \cdot \sqrt{72})}^{2}$

Rewrite $\sqrt{- 1}$ as $i$ .

${(i \cdot \sqrt{72})}^{2}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

${(i \cdot \sqrt{36 (2)})}^{2}$

Rewrite $36$ as $6^{2}$ .

${(i \cdot \sqrt{6^{2} \cdot 2})}^{2}$

Pull terms out from under the radical.

${(i \cdot (6 \sqrt{2}))}^{2}$

Move $6$ to the left of $i$ .

${(6 \cdot i \sqrt{2})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $6 i \sqrt{2}$ .

${(6 i)}^{2} {\sqrt{2}}^{2}$

Apply the product rule to $6 i$ .

$6^{2} i^{2} {\sqrt{2}}^{2}$

Raise $6$ to the power of $2$ .

$36 i^{2} {\sqrt{2}}^{2}$

Rewrite $i^{2}$ as $- 1$ .

$36 \cdot - 1 {\sqrt{2}}^{2}$

Multiply $36$ by $- 1$ .

$- 36 {\sqrt{2}}^{2}$

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

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

$- 36 {(2^{\frac{1}{2}})}^{2}$

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

$- 36 \cdot 2^{\frac{1}{2} \cdot 2}$

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

$- 36 \cdot 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 36 \cdot 2^{\frac{2}{2}}$

Rewrite the expression.

$- 36 \cdot 2^{1}$

Evaluate the exponent.

$- 36 \cdot 2$

Multiply $- 36$ by $2$ .

$- 72$