Trigonometry Examples

$\sqrt{- \frac{49}{149}}$

Step 1

Rewrite $- \frac{49}{149}$ as $i^{2} \frac{7^{2}}{149}$ .

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Step 1.1

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

$\sqrt{i^{2} \frac{49}{149}}$

Step 1.2

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

$\sqrt{i^{2} \frac{7^{2}}{149}}$

Step 2

Pull terms out from under the radical.

$i \sqrt{\frac{7^{2}}{149}}$

Step 3

Raise $7$ to the power of $2$ .

$i \sqrt{\frac{49}{149}}$

Step 4

Rewrite $\sqrt{\frac{49}{149}}$ as $\frac{\sqrt{49}}{\sqrt{149}}$ .

$i \frac{\sqrt{49}}{\sqrt{149}}$

Step 5

Simplify the numerator.

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Step 5.1

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

$i \frac{\sqrt{7^{2}}}{\sqrt{149}}$

Step 5.2

Pull terms out from under the radical, assuming positive real numbers.

$i \frac{7}{\sqrt{149}}$

Step 6

Multiply $\frac{7}{\sqrt{149}}$ by $\frac{\sqrt{149}}{\sqrt{149}}$ .

$i (\frac{7}{\sqrt{149}} \cdot \frac{\sqrt{149}}{\sqrt{149}})$

Step 7

Combine and simplify the denominator.

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Step 7.1

Multiply $\frac{7}{\sqrt{149}}$ by $\frac{\sqrt{149}}{\sqrt{149}}$ .

$i \frac{7 \sqrt{149}}{\sqrt{149} \sqrt{149}}$

Step 7.2

Raise $\sqrt{149}$ to the power of $1$ .

$i \frac{7 \sqrt{149}}{{\sqrt{149}}^{1} \sqrt{149}}$

Step 7.3

Raise $\sqrt{149}$ to the power of $1$ .

$i \frac{7 \sqrt{149}}{{\sqrt{149}}^{1} {\sqrt{149}}^{1}}$

Step 7.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$i \frac{7 \sqrt{149}}{{\sqrt{149}}^{1 + 1}}$

Step 7.5

Add $1$ and $1$ .

$i \frac{7 \sqrt{149}}{{\sqrt{149}}^{2}}$

Step 7.6

Rewrite ${\sqrt{149}}^{2}$ as $149$ .

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Step 7.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{149}$ as $149^{\frac{1}{2}}$ .

$i \frac{7 \sqrt{149}}{{(149^{\frac{1}{2}})}^{2}}$

Step 7.6.2

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

$i \frac{7 \sqrt{149}}{149^{\frac{1}{2} \cdot 2}}$

Step 7.6.3

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

$i \frac{7 \sqrt{149}}{149^{\frac{2}{2}}}$

Step 7.6.4

Cancel the common factor of $2$ .

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Step 7.6.4.1

Cancel the common factor.

$i \frac{7 \sqrt{149}}{149^{\frac{2}{2}}}$

Step 7.6.4.2

Rewrite the expression.

$i \frac{7 \sqrt{149}}{149^{1}}$

Step 7.6.5

Evaluate the exponent.

$i \frac{7 \sqrt{149}}{149}$

Step 8

Combine $i$ and $\frac{7 \sqrt{149}}{149}$ .

$\frac{i (7 \sqrt{149})}{149}$

Step 9

Move $7$ to the left of $i$ .

$\frac{7 i \sqrt{149}}{149}$