Trigonometry Examples

$\sqrt{\frac{\sqrt{26}}{26}}$

Step 1

Rewrite $\sqrt{\frac{\sqrt{26}}{26}}$ as $\frac{\sqrt{\sqrt{26}}}{\sqrt{26}}$ .

$\frac{\sqrt{\sqrt{26}}}{\sqrt{26}}$

Step 2

Rewrite $\sqrt{\sqrt{26}}$ as $\sqrt[4]{26}$ .

$\frac{\sqrt[4]{26}}{\sqrt{26}}$

Step 3

Multiply $\frac{\sqrt[4]{26}}{\sqrt{26}}$ by $\frac{\sqrt{26}}{\sqrt{26}}$ .

$\frac{\sqrt[4]{26}}{\sqrt{26}} \cdot \frac{\sqrt{26}}{\sqrt{26}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{\sqrt[4]{26}}{\sqrt{26}}$ by $\frac{\sqrt{26}}{\sqrt{26}}$ .

$\frac{\sqrt[4]{26} \sqrt{26}}{\sqrt{26} \sqrt{26}}$

Step 4.2

Raise $\sqrt{26}$ to the power of $1$ .

$\frac{\sqrt[4]{26} \sqrt{26}}{{\sqrt{26}}^{1} \sqrt{26}}$

Step 4.3

Raise $\sqrt{26}$ to the power of $1$ .

$\frac{\sqrt[4]{26} \sqrt{26}}{{\sqrt{26}}^{1} {\sqrt{26}}^{1}}$

Step 4.4

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

$\frac{\sqrt[4]{26} \sqrt{26}}{{\sqrt{26}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$\frac{\sqrt[4]{26} \sqrt{26}}{{\sqrt{26}}^{2}}$

Step 4.6

Rewrite ${\sqrt{26}}^{2}$ as $26$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{26}$ as $26^{\frac{1}{2}}$ .

$\frac{\sqrt[4]{26} \sqrt{26}}{{(26^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$\frac{\sqrt[4]{26} \sqrt{26}}{26^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$\frac{\sqrt[4]{26} \sqrt{26}}{26^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{\sqrt[4]{26} \sqrt{26}}{26^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$\frac{\sqrt[4]{26} \sqrt{26}}{26^{1}}$

Step 4.6.5

Evaluate the exponent.

$\frac{\sqrt[4]{26} \sqrt{26}}{26}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite the expression using the least common index of $4$ .

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Step 5.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{26}$ as $26^{\frac{1}{2}}$ .

$\frac{\sqrt[4]{26} \cdot 26^{\frac{1}{2}}}{26}$

Step 5.1.2

Rewrite $26^{\frac{1}{2}}$ as $26^{\frac{2}{4}}$ .

$\frac{\sqrt[4]{26} \cdot 26^{\frac{2}{4}}}{26}$

Step 5.1.3

Rewrite $26^{\frac{2}{4}}$ as $\sqrt[4]{26^{2}}$ .

$\frac{\sqrt[4]{26} \sqrt[4]{26^{2}}}{26}$

Step 5.2

Combine using the product rule for radicals.

$\frac{\sqrt[4]{26 \cdot 26^{2}}}{26}$

Step 5.3

Multiply $26$ by $26^{2}$ by adding the exponents.

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Step 5.3.1

Multiply $26$ by $26^{2}$ .

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Step 5.3.1.1

Raise $26$ to the power of $1$ .

$\frac{\sqrt[4]{26^{1} \cdot 26^{2}}}{26}$

Step 5.3.1.2

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

$\frac{\sqrt[4]{26^{1 + 2}}}{26}$

Step 5.3.2

Add $1$ and $2$ .

$\frac{\sqrt[4]{26^{3}}}{26}$

Step 6

Raise $26$ to the power of $3$ .

$\frac{\sqrt[4]{17576}}{26}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[4]{17576}}{26}$

Decimal Form:

$0.44285001 \dots$