Finite Math Examples

$\frac{15 - \sqrt{75}}{35}$

Step 1

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

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Step 1.1

Factor $25$ out of $75$ .

$\frac{15 - \sqrt{25 (3)}}{35}$

Step 1.2

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

$\frac{15 - \sqrt{5^{2} \cdot 3}}{35}$

Step 2

Pull terms out from under the radical.

$\frac{15 - (5 \sqrt{3})}{35}$

Step 3

Multiply $5$ by $- 1$ .

$\frac{15 - 5 \sqrt{3}}{35}$

Step 4

Reduce the expression $\frac{15 - 5 \sqrt{3}}{35}$ by cancelling the common factors.

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Step 4.1

Factor $5$ out of $15$ .

$\frac{5 (3) - 5 \sqrt{3}}{35}$

Step 4.2

Factor $5$ out of $- 5 \sqrt{3}$ .

$\frac{5 (3) + 5 (- \sqrt{3})}{35}$

Step 4.3

Factor $5$ out of $5 (3) + 5 (- \sqrt{3})$ .

$\frac{5 (3 - \sqrt{3})}{35}$

Step 4.4

Factor $5$ out of $35$ .

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

Step 4.5

Cancel the common factor.

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

Step 4.6

Rewrite the expression.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.18113559 \dots$