Basic Math Examples

$4 \cdot \sqrt{\frac{75}{49}} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sqrt{\frac{75}{49}}$ as $\frac{\sqrt{75}}{\sqrt{49}}$ .

$4 \cdot \frac{\sqrt{75}}{\sqrt{49}} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.2.1.1

Factor $25$ out of $75$ .

$4 \cdot \frac{\sqrt{25 (3)}}{\sqrt{49}} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1.2.1.2

Rewrite $25$ as $5^{2}$ .

$4 \cdot \frac{\sqrt{5^{2} \cdot 3}}{\sqrt{49}} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1.2.2

Pull terms out from under the radical.

$4 \cdot \frac{5 \sqrt{3}}{\sqrt{49}} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

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

$4 \cdot \frac{5 \sqrt{3}}{\sqrt{7^{2}}} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1.3.2

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

$4 \cdot \frac{5 \sqrt{3}}{7} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1.4

Multiply $4 \frac{5 \sqrt{3}}{7}$ .

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Step 1.4.1

Combine $4$ and $\frac{5 \sqrt{3}}{7}$ .

$\frac{4 (5 \sqrt{3})}{7} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1.4.2

Multiply $5$ by $4$ .

$\frac{20 \sqrt{3}}{7} - \frac{\sqrt{8}}{\sqrt{18}}$

Step 1.5

Combine $\sqrt{8}$ and $\sqrt{18}$ into a single radical.

$\frac{20 \sqrt{3}}{7} - \sqrt{\frac{8}{18}}$

Step 1.6

Cancel the common factor of $8$ and $18$ .

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Step 1.6.1

Factor $2$ out of $8$ .

$\frac{20 \sqrt{3}}{7} - \sqrt{\frac{2 (4)}{18}}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $18$ .

$\frac{20 \sqrt{3}}{7} - \sqrt{\frac{2 \cdot 4}{2 \cdot 9}}$

Step 1.6.2.2

Cancel the common factor.

$\frac{20 \sqrt{3}}{7} - \sqrt{\frac{2 \cdot 4}{2 \cdot 9}}$

Step 1.6.2.3

Rewrite the expression.

$\frac{20 \sqrt{3}}{7} - \sqrt{\frac{4}{9}}$

Step 1.7

Rewrite $\sqrt{\frac{4}{9}}$ as $\frac{\sqrt{4}}{\sqrt{9}}$ .

$\frac{20 \sqrt{3}}{7} - \frac{\sqrt{4}}{\sqrt{9}}$

Step 1.8

Simplify the numerator.

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Step 1.8.1

Rewrite $4$ as $2^{2}$ .

$\frac{20 \sqrt{3}}{7} - \frac{\sqrt{2^{2}}}{\sqrt{9}}$

Step 1.8.2

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

$\frac{20 \sqrt{3}}{7} - \frac{2}{\sqrt{9}}$

Step 1.9

Simplify the denominator.

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Step 1.9.1

Rewrite $9$ as $3^{2}$ .

$\frac{20 \sqrt{3}}{7} - \frac{2}{\sqrt{3^{2}}}$

Step 1.9.2

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

$\frac{20 \sqrt{3}}{7} - \frac{2}{3}$

Step 2

To write $\frac{20 \sqrt{3}}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{20 \sqrt{3}}{7} \cdot \frac{3}{3} - \frac{2}{3}$

Step 3

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{20 \sqrt{3}}{7} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{20 \sqrt{3}}{7}$ by $\frac{3}{3}$ .

$\frac{20 \sqrt{3} \cdot 3}{7 \cdot 3} - \frac{2}{3} \cdot \frac{7}{7}$

Step 4.2

Multiply $7$ by $3$ .

$\frac{20 \sqrt{3} \cdot 3}{21} - \frac{2}{3} \cdot \frac{7}{7}$

Step 4.3

Multiply $\frac{2}{3}$ by $\frac{7}{7}$ .

$\frac{20 \sqrt{3} \cdot 3}{21} - \frac{2 \cdot 7}{3 \cdot 7}$

Step 4.4

Multiply $3$ by $7$ .

$\frac{20 \sqrt{3} \cdot 3}{21} - \frac{2 \cdot 7}{21}$

Step 5

Combine the numerators over the common denominator.

$\frac{20 \sqrt{3} \cdot 3 - 2 \cdot 7}{21}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $20$ .

$\frac{60 \sqrt{3} - 2 \cdot 7}{21}$

Step 6.2

Multiply $- 2$ by $7$ .

$\frac{60 \sqrt{3} - 14}{21}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{60 \sqrt{3} - 14}{21}$

Decimal Form:

$4.28204992 \dots$