Basic Math Examples

$\frac{\sqrt[3]{\frac{343}{64}}}{\sqrt{\frac{100}{121}}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $\sqrt[3]{\frac{343}{64}}$ as $\frac{\sqrt[3]{343}}{\sqrt[3]{64}}$ .

$\frac{\frac{\sqrt[3]{343}}{\sqrt[3]{64}}}{\sqrt{\frac{100}{121}}}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Rewrite $343$ as $7^{3}$ .

$\frac{\frac{\sqrt[3]{7^{3}}}{\sqrt[3]{64}}}{\sqrt{\frac{100}{121}}}$

Step 1.2.2

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

$\frac{\frac{7}{\sqrt[3]{64}}}{\sqrt{\frac{100}{121}}}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $64$ as $4^{3}$ .

$\frac{\frac{7}{\sqrt[3]{4^{3}}}}{\sqrt{\frac{100}{121}}}$

Step 1.3.2

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

$\frac{\frac{7}{4}}{\sqrt{\frac{100}{121}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $\sqrt{\frac{100}{121}}$ as $\frac{\sqrt{100}}{\sqrt{121}}$ .

$\frac{\frac{7}{4}}{\frac{\sqrt{100}}{\sqrt{121}}}$

Step 2.2

Simplify the numerator.

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Step 2.2.1

Rewrite $100$ as $10^{2}$ .

$\frac{\frac{7}{4}}{\frac{\sqrt{10^{2}}}{\sqrt{121}}}$

Step 2.2.2

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

$\frac{\frac{7}{4}}{\frac{10}{\sqrt{121}}}$

Step 2.3

Simplify the denominator.

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Step 2.3.1

Rewrite $121$ as $11^{2}$ .

$\frac{\frac{7}{4}}{\frac{10}{\sqrt{11^{2}}}}$

Step 2.3.2

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

$\frac{\frac{7}{4}}{\frac{10}{11}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{7}{4} \cdot \frac{11}{10}$

Step 4

Multiply $\frac{7}{4} \cdot \frac{11}{10}$ .

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Step 4.1

Multiply $\frac{7}{4}$ by $\frac{11}{10}$ .

$\frac{7 \cdot 11}{4 \cdot 10}$

Step 4.2

Multiply $7$ by $11$ .

$\frac{77}{4 \cdot 10}$

Step 4.3

Multiply $4$ by $10$ .

$\frac{77}{40}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{77}{40}$

Decimal Form:

$1.925$

Mixed Number Form:

$1 \frac{37}{40}$