Basic Math Examples

$(5 \sqrt{50} - 10 \sqrt{18}) \div 5 \sqrt{2}$

Step 1

Rewrite the division as a fraction.

$\frac{5 \sqrt{50} - 10 \sqrt{18}}{5 \sqrt{2}}$

Step 2

Cancel the common factor of $5 \sqrt{50} - 10 \sqrt{18}$ and $5$ .

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Step 2.1

Factor $5$ out of $5 \sqrt{50}$ .

$\frac{5 (\sqrt{50}) - 10 \sqrt{18}}{5 \sqrt{2}}$

Step 2.2

Factor $5$ out of $- 10 \sqrt{18}$ .

$\frac{5 (\sqrt{50}) + 5 (- 2 \sqrt{18})}{5 \sqrt{2}}$

Step 2.3

Factor $5$ out of $5 (\sqrt{50}) + 5 (- 2 \sqrt{18})$ .

$\frac{5 (\sqrt{50} - 2 \sqrt{18})}{5 \sqrt{2}}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $5$ out of $5 \sqrt{2}$ .

$\frac{5 (\sqrt{50} - 2 \sqrt{18})}{5 (\sqrt{2})}$

Step 2.4.2

Cancel the common factor.

$\frac{5 (\sqrt{50} - 2 \sqrt{18})}{5 \sqrt{2}}$

Step 2.4.3

Rewrite the expression.

$\frac{\sqrt{50} - 2 \sqrt{18}}{\sqrt{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 3.1.1

Factor $25$ out of $50$ .

$\frac{\sqrt{25 (2)} - 2 \sqrt{18}}{\sqrt{2}}$

Step 3.1.2

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

$\frac{\sqrt{5^{2} \cdot 2} - 2 \sqrt{18}}{\sqrt{2}}$

Step 3.2

Pull terms out from under the radical.

$\frac{5 \sqrt{2} - 2 \sqrt{18}}{\sqrt{2}}$

Step 3.3

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 3.3.1

Factor $9$ out of $18$ .

$\frac{5 \sqrt{2} - 2 \sqrt{9 (2)}}{\sqrt{2}}$

Step 3.3.2

Rewrite $9$ as $3^{2}$ .

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

Step 3.4

Pull terms out from under the radical.

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

Step 3.5

Multiply $3$ by $- 2$ .

$\frac{5 \sqrt{2} - 6 \sqrt{2}}{\sqrt{2}}$

Step 3.6

Subtract $6 \sqrt{2}$ from $5 \sqrt{2}$ .

$\frac{- \sqrt{2}}{\sqrt{2}}$

Step 4

Cancel the common factor of $\sqrt{2}$ .

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Step 4.1

Cancel the common factor.

$\frac{- \sqrt{2}}{\sqrt{2}}$

Step 4.2

Divide $- 1$ by $1$ .

$- 1$