Trigonometry Examples

\sqrt{\frac{\frac{10}{7}}{2}}

$\sqrt{\frac{\frac{10}{7}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

\sqrt{\frac{10}{7} \cdot \frac{1}{2}}

$\sqrt{\frac{10}{7} \cdot \frac{1}{2}}$

Step 2

Cancel the common factor of

2

$2$ .

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Step 2.1

Factor

2

$2$ out of

10

$10$ .

\sqrt{\frac{2 (5)}{7} \cdot \frac{1}{2}}

$\sqrt{\frac{2 (5)}{7} \cdot \frac{1}{2}}$

Step 2.2

Cancel the common factor.

$\sqrt{\frac{2 \cdot 5}{7} \cdot \frac{1}{2}}$

Step 2.3

Rewrite the expression.

$\sqrt{\frac{5}{7}}$

Step 3

Rewrite

$\sqrt{\frac{5}{7}}$ as

$\frac{\sqrt{5}}{\sqrt{7}}$ .

$\frac{\sqrt{5}}{\sqrt{7}}$

Step 4

Multiply

$\frac{\sqrt{5}}{\sqrt{7}}$ by

$\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt{5}}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply

$\frac{\sqrt{5}}{\sqrt{7}}$ by

$\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\sqrt{5} \sqrt{7}}{\sqrt{7} \sqrt{7}}$

Step 5.2

Raise

$\sqrt{7}$ to the power of

$1$ .

$\frac{\sqrt{5} \sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Step 5.3

Raise

$\sqrt{7}$ to the power of

$1$ .

$\frac{\sqrt{5} \sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

Step 5.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{5} \sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Step 5.5

Add

$1$ and

$1$ .

$\frac{\sqrt{5} \sqrt{7}}{{\sqrt{7}}^{2}}$

Step 5.6

Rewrite

${\sqrt{7}}^{2}$ as

$7$ .

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Step 5.6.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{7}$ as

$7^{\frac{1}{2}}$ .

$\frac{\sqrt{5} \sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}$

Step 5.6.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{5} \sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

Step 5.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\frac{\sqrt{5} \sqrt{7}}{7^{\frac{2}{2}}}$

Step 5.6.4

Cancel the common factor of

$2$ .

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Step 5.6.4.1

Cancel the common factor.

$\frac{\sqrt{5} \sqrt{7}}{7^{\frac{2}{2}}}$

Step 5.6.4.2

Rewrite the expression.

$\frac{\sqrt{5} \sqrt{7}}{7^{1}}$

Step 5.6.5

Evaluate the exponent.

$\frac{\sqrt{5} \sqrt{7}}{7}$

Step 6

Simplify the numerator.

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Step 6.1

Combine using the product rule for radicals.

$\frac{\sqrt{5 \cdot 7}}{7}$

Step 6.2

Multiply

$5$ by

$7$ .

$\frac{\sqrt{35}}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{35}}{7}$

Decimal Form:

$0.84515425 \dots$