Precalculus Examples

${(\sqrt{- 75})}^{2}$

Step 1

Rewrite $- 75$ as $- 1 (75)$ .

${\sqrt{- 1 (75)}}^{2}$

Step 2

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

${(\sqrt{- 1} \cdot \sqrt{75})}^{2}$

Step 3

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

${(i \cdot \sqrt{75})}^{2}$

Step 4

Rewrite $75$ as $5^{2} \cdot 3$ .

Tap for more steps...

Step 4.1

Factor $25$ out of $75$ .

${(i \cdot \sqrt{25 (3)})}^{2}$

Step 4.2

Rewrite $25$ as $5^{2}$ .

${(i \cdot \sqrt{5^{2} \cdot 3})}^{2}$

Step 5

Pull terms out from under the radical.

${(i \cdot (5 \sqrt{3}))}^{2}$

Step 6

Move $5$ to the left of $i$ .

${(5 \cdot i \sqrt{3})}^{2}$

Step 7

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

Tap for more steps...

Step 7.1

Apply the product rule to $5 i \sqrt{3}$ .

${(5 i)}^{2} {\sqrt{3}}^{2}$

Step 7.2

Apply the product rule to $5 i$ .

$5^{2} i^{2} {\sqrt{3}}^{2}$

Step 8

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

$25 i^{2} {\sqrt{3}}^{2}$

Step 9

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

$25 \cdot - 1 {\sqrt{3}}^{2}$

Step 10

Multiply $25$ by $- 1$ .

$- 25 {\sqrt{3}}^{2}$

Step 11

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Tap for more steps...

Step 11.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$- 25 {(3^{\frac{1}{2}})}^{2}$

Step 11.2

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

$- 25 \cdot 3^{\frac{1}{2} \cdot 2}$

Step 11.3

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

$- 25 \cdot 3^{\frac{2}{2}}$

Step 11.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 11.4.1

Cancel the common factor.

$- 25 \cdot 3^{\frac{2}{2}}$

Step 11.4.2

Rewrite the expression.

$- 25 \cdot 3^{1}$

Step 11.5

Evaluate the exponent.

$- 25 \cdot 3$

Step 12

Multiply $- 25$ by $3$ .

$- 75$