Finite Math Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

Multiply $\frac{20 \sqrt{2}}{\sqrt{7} - \sqrt{3}}$ by $\frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} + \sqrt{3}}$ .

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

Step 3

Multiply $\frac{20 \sqrt{2}}{\sqrt{7} - \sqrt{3}}$ by $\frac{\sqrt{7} + \sqrt{3}}{\sqrt{7} + \sqrt{3}}$ .

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

Step 4

Expand the denominator using the FOIL method.

$- \frac{20 \sqrt{2} (\sqrt{7} + \sqrt{3})}{{\sqrt{7}}^{2} + \sqrt{21} - \sqrt{21} - {\sqrt{3}}^{2}}$

Step 5

Simplify.

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

Step 6

Cancel the common factor of $20$ and $4$ .

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Step 6.1

Factor $4$ out of $20 \sqrt{2} (\sqrt{7} + \sqrt{3})$ .

$- \frac{4 (5 \sqrt{2} (\sqrt{7} + \sqrt{3}))}{4}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $4$ out of $4$ .

$- \frac{4 (5 \sqrt{2} (\sqrt{7} + \sqrt{3}))}{4 (1)}$

Step 6.2.2

Cancel the common factor.

$- \frac{4 (5 \sqrt{2} (\sqrt{7} + \sqrt{3}))}{4 \cdot 1}$

Step 6.2.3

Rewrite the expression.

$- \frac{5 \sqrt{2} (\sqrt{7} + \sqrt{3})}{1}$

Step 6.2.4

Divide $5 \sqrt{2} (\sqrt{7} + \sqrt{3})$ by $1$ .

$- (5 \sqrt{2} (\sqrt{7} + \sqrt{3}))$

Step 7

Apply the distributive property.

$- (5 \sqrt{2} \sqrt{7} + 5 \sqrt{2} \sqrt{3})$

Step 8

Multiply $5 \sqrt{2} \sqrt{7}$ .

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Step 8.1

Combine using the product rule for radicals.

$- (5 \sqrt{7 \cdot 2} + 5 \sqrt{2} \sqrt{3})$

Step 8.2

Multiply $7$ by $2$ .

$- (5 \sqrt{14} + 5 \sqrt{2} \sqrt{3})$

Step 9

Multiply $5 \sqrt{2} \sqrt{3}$ .

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Step 9.1

Combine using the product rule for radicals.

$- (5 \sqrt{14} + 5 \sqrt{3 \cdot 2})$

Step 9.2

Multiply $3$ by $2$ .

$- (5 \sqrt{14} + 5 \sqrt{6})$

Step 10

Apply the distributive property.

$- (5 \sqrt{14}) - (5 \sqrt{6})$

Step 11

Multiply.

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Step 11.1

Multiply $5$ by $- 1$ .

$- 5 \sqrt{14} - (5 \sqrt{6})$

Step 11.2

Multiply $5$ by $- 1$ .

$- 5 \sqrt{14} - 5 \sqrt{6}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- 5 \sqrt{14} - 5 \sqrt{6}$

Decimal Form:

$- 30.95573564 \dots$