Basic Math Examples

$(7 \sqrt{3} - 5 \sqrt{48} + 2 \sqrt{192}) \div 3 \sqrt{3}$

Step 1

Rewrite the division as a fraction.

$\frac{7 \sqrt{3} - 5 \sqrt{48} + 2 \sqrt{192}}{3 \sqrt{3}}$

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

Factor $16$ out of $48$ .

$\frac{7 \sqrt{3} - 5 \sqrt{16 (3)} + 2 \sqrt{192}}{3 \sqrt{3}}$

Step 2.1.2

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

$\frac{7 \sqrt{3} - 5 \sqrt{4^{2} \cdot 3} + 2 \sqrt{192}}{3 \sqrt{3}}$

Step 2.2

Pull terms out from under the radical.

$\frac{7 \sqrt{3} - 5 (4 \sqrt{3}) + 2 \sqrt{192}}{3 \sqrt{3}}$

Step 2.3

Multiply $4$ by $- 5$ .

$\frac{7 \sqrt{3} - 20 \sqrt{3} + 2 \sqrt{192}}{3 \sqrt{3}}$

Step 2.4

Rewrite $192$ as $8^{2} \cdot 3$ .

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Step 2.4.1

Factor $64$ out of $192$ .

$\frac{7 \sqrt{3} - 20 \sqrt{3} + 2 \sqrt{64 (3)}}{3 \sqrt{3}}$

Step 2.4.2

Rewrite $64$ as $8^{2}$ .

$\frac{7 \sqrt{3} - 20 \sqrt{3} + 2 \sqrt{8^{2} \cdot 3}}{3 \sqrt{3}}$

Step 2.5

Pull terms out from under the radical.

$\frac{7 \sqrt{3} - 20 \sqrt{3} + 2 (8 \sqrt{3})}{3 \sqrt{3}}$

Step 2.6

Multiply $8$ by $2$ .

$\frac{7 \sqrt{3} - 20 \sqrt{3} + 16 \sqrt{3}}{3 \sqrt{3}}$

Step 2.7

Subtract $20 \sqrt{3}$ from $7 \sqrt{3}$ .

$\frac{- 13 \sqrt{3} + 16 \sqrt{3}}{3 \sqrt{3}}$

Step 2.8

Add $- 13 \sqrt{3}$ and $16 \sqrt{3}$ .

$\frac{3 \sqrt{3}}{3 \sqrt{3}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Cancel the common factor.

$\frac{3 \sqrt{3}}{3 \sqrt{3}}$

Step 3.1.2

Rewrite the expression.

$\frac{\sqrt{3}}{\sqrt{3}}$

Step 3.2

Cancel the common factor of $\sqrt{3}$ .

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Step 3.2.1

Cancel the common factor.

$\frac{\sqrt{3}}{\sqrt{3}}$

Step 3.2.2

Rewrite the expression.

$1$