Basic Math Examples

$\sqrt[4]{58} \div \sqrt[4]{52}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt[4]{58}}{\sqrt[4]{52}}$

Step 2

Combine $\sqrt[4]{58}$ and $\sqrt[4]{52}$ into a single radical.

$\sqrt[4]{\frac{58}{52}}$

Step 3

Cancel the common factor of $58$ and $52$ .

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Step 3.1

Factor $2$ out of $58$ .

$\sqrt[4]{\frac{2 (29)}{52}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $52$ .

$\sqrt[4]{\frac{2 \cdot 29}{2 \cdot 26}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[4]{\frac{2 \cdot 29}{2 \cdot 26}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[4]{\frac{29}{26}}$

Step 4

Rewrite $\sqrt[4]{\frac{29}{26}}$ as $\frac{\sqrt[4]{29}}{\sqrt[4]{26}}$ .

$\frac{\sqrt[4]{29}}{\sqrt[4]{26}}$

Step 5

Multiply $\frac{\sqrt[4]{29}}{\sqrt[4]{26}}$ by $\frac{{\sqrt[4]{26}}^{3}}{{\sqrt[4]{26}}^{3}}$ .

$\frac{\sqrt[4]{29}}{\sqrt[4]{26}} \cdot \frac{{\sqrt[4]{26}}^{3}}{{\sqrt[4]{26}}^{3}}$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{\sqrt[4]{29}}{\sqrt[4]{26}}$ by $\frac{{\sqrt[4]{26}}^{3}}{{\sqrt[4]{26}}^{3}}$ .

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{\sqrt[4]{26} {\sqrt[4]{26}}^{3}}$

Step 6.2

Raise $\sqrt[4]{26}$ to the power of $1$ .

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{{\sqrt[4]{26}}^{1} {\sqrt[4]{26}}^{3}}$

Step 6.3

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

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{{\sqrt[4]{26}}^{1 + 3}}$

Step 6.4

Add $1$ and $3$ .

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{{\sqrt[4]{26}}^{4}}$

Step 6.5

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

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Step 6.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{26}$ as $26^{\frac{1}{4}}$ .

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{{(26^{\frac{1}{4}})}^{4}}$

Step 6.5.2

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

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{26^{\frac{1}{4} \cdot 4}}$

Step 6.5.3

Combine $\frac{1}{4}$ and $4$ .

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{26^{\frac{4}{4}}}$

Step 6.5.4

Cancel the common factor of $4$ .

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Step 6.5.4.1

Cancel the common factor.

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{26^{\frac{4}{4}}}$

Step 6.5.4.2

Rewrite the expression.

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{26^{1}}$

Step 6.5.5

Evaluate the exponent.

$\frac{\sqrt[4]{29} {\sqrt[4]{26}}^{3}}{26}$

Step 7

Simplify the numerator.

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Step 7.1

Rewrite ${\sqrt[4]{26}}^{3}$ as $\sqrt[4]{26^{3}}$ .

$\frac{\sqrt[4]{29} \sqrt[4]{26^{3}}}{26}$

Step 7.2

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

$\frac{\sqrt[4]{29} \sqrt[4]{17576}}{26}$

Step 8

Simplify the numerator.

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Step 8.1

Combine using the product rule for radicals.

$\frac{\sqrt[4]{29 \cdot 17576}}{26}$

Step 8.2

Multiply $29$ by $17576$ .

$\frac{\sqrt[4]{509704}}{26}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[4]{509704}}{26}$

Decimal Form:

$1.02767587 \dots$