Finite Math Examples

$\frac{1}{4} \cdot \sqrt{288} - \frac{1}{6} \cdot \sqrt{72}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $288$ as $12^{2} \cdot 2$ .

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Step 1.1.1

Factor $144$ out of $288$ .

$\frac{1}{4} \cdot \sqrt{144 (2)} - \frac{1}{6} \cdot \sqrt{72}$

Step 1.1.2

Rewrite $144$ as $12^{2}$ .

$\frac{1}{4} \cdot \sqrt{12^{2} \cdot 2} - \frac{1}{6} \cdot \sqrt{72}$

Step 1.2

Pull terms out from under the radical.

$\frac{1}{4} \cdot (12 \sqrt{2}) - \frac{1}{6} \cdot \sqrt{72}$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $12 \sqrt{2}$ .

$\frac{1}{4} \cdot (4 (3 \sqrt{2})) - \frac{1}{6} \cdot \sqrt{72}$

Step 1.3.2

Cancel the common factor.

$\frac{1}{4} \cdot (4 (3 \sqrt{2})) - \frac{1}{6} \cdot \sqrt{72}$

Step 1.3.3

Rewrite the expression.

$3 \sqrt{2} - \frac{1}{6} \cdot \sqrt{72}$

Step 1.4

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.4.1

Factor $36$ out of $72$ .

$3 \sqrt{2} - \frac{1}{6} \cdot \sqrt{36 (2)}$

Step 1.4.2

Rewrite $36$ as $6^{2}$ .

$3 \sqrt{2} - \frac{1}{6} \cdot \sqrt{6^{2} \cdot 2}$

Step 1.5

Pull terms out from under the radical.

$3 \sqrt{2} - \frac{1}{6} \cdot (6 \sqrt{2})$

Step 1.6

Cancel the common factor of $6$ .

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Step 1.6.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$3 \sqrt{2} + \frac{- 1}{6} \cdot (6 \sqrt{2})$

Step 1.6.2

Factor $6$ out of $6 \sqrt{2}$ .

$3 \sqrt{2} + \frac{- 1}{6} \cdot (6 (\sqrt{2}))$

Step 1.6.3

Cancel the common factor.

$3 \sqrt{2} + \frac{- 1}{6} \cdot (6 \sqrt{2})$

Step 1.6.4

Rewrite the expression.

$3 \sqrt{2} - 1 \cdot \sqrt{2}$

Step 1.7

Rewrite $- 1 \sqrt{2}$ as $- \sqrt{2}$ .

$3 \sqrt{2} - \sqrt{2}$

Step 2

Subtract $\sqrt{2}$ from $3 \sqrt{2}$ .

$2 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$