Basic Math Examples

$\frac{1}{4} \cdot \sqrt{48} + \frac{375}{100} \cdot \sqrt{48}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 1.1.1

Factor $16$ out of $48$ .

$\frac{1}{4} \cdot \sqrt{16 (3)} + \frac{375}{100} \cdot \sqrt{48}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{1}{4} \cdot \sqrt{4^{2} \cdot 3} + \frac{375}{100} \cdot \sqrt{48}$

Step 1.2

Pull terms out from under the radical.

$\frac{1}{4} \cdot (4 \sqrt{3}) + \frac{375}{100} \cdot \sqrt{48}$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $4 \sqrt{3}$ .

$\frac{1}{4} \cdot (4 (\sqrt{3})) + \frac{375}{100} \cdot \sqrt{48}$

Step 1.3.2

Cancel the common factor.

$\frac{1}{4} \cdot (4 \sqrt{3}) + \frac{375}{100} \cdot \sqrt{48}$

Step 1.3.3

Rewrite the expression.

$\sqrt{3} + \frac{375}{100} \cdot \sqrt{48}$

Step 1.4

Cancel the common factor of $375$ and $100$ .

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Step 1.4.1

Factor $25$ out of $375$ .

$\sqrt{3} + \frac{25 (15)}{100} \cdot \sqrt{48}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $25$ out of $100$ .

$\sqrt{3} + \frac{25 \cdot 15}{25 \cdot 4} \cdot \sqrt{48}$

Step 1.4.2.2

Cancel the common factor.

$\sqrt{3} + \frac{25 \cdot 15}{25 \cdot 4} \cdot \sqrt{48}$

Step 1.4.2.3

Rewrite the expression.

$\sqrt{3} + \frac{15}{4} \cdot \sqrt{48}$

Step 1.5

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 1.5.1

Factor $16$ out of $48$ .

$\sqrt{3} + \frac{15}{4} \cdot \sqrt{16 (3)}$

Step 1.5.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{3} + \frac{15}{4} \cdot \sqrt{4^{2} \cdot 3}$

Step 1.6

Pull terms out from under the radical.

$\sqrt{3} + \frac{15}{4} \cdot (4 \sqrt{3})$

Step 1.7

Cancel the common factor of $4$ .

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Step 1.7.1

Factor $4$ out of $4 \sqrt{3}$ .

$\sqrt{3} + \frac{15}{4} \cdot (4 (\sqrt{3}))$

Step 1.7.2

Cancel the common factor.

$\sqrt{3} + \frac{15}{4} \cdot (4 \sqrt{3})$

Step 1.7.3

Rewrite the expression.

$\sqrt{3} + 15 \cdot \sqrt{3}$

$\sqrt{3} + 15 \sqrt{3}$

Step 2

Add $\sqrt{3}$ and $15 \sqrt{3}$ .

$16 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$16 \sqrt{3}$

Decimal Form:

$27.71281292 \dots$