Basic Math Examples

$\frac{\sqrt{200}}{3} - \frac{\sqrt{50}}{4}$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Rewrite $200$ as $10^{2} \cdot 2$ .

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Step 1.1.1.1

Factor $100$ out of $200$ .

$\frac{\sqrt{100 (2)}}{3} - \frac{\sqrt{50}}{4}$

Step 1.1.1.2

Rewrite $100$ as $10^{2}$ .

$\frac{\sqrt{10^{2} \cdot 2}}{3} - \frac{\sqrt{50}}{4}$

Step 1.1.2

Pull terms out from under the radical.

$\frac{10 \sqrt{2}}{3} - \frac{\sqrt{50}}{4}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

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

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Step 1.2.1.1

Factor $25$ out of $50$ .

$\frac{10 \sqrt{2}}{3} - \frac{\sqrt{25 (2)}}{4}$

Step 1.2.1.2

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

$\frac{10 \sqrt{2}}{3} - \frac{\sqrt{5^{2} \cdot 2}}{4}$

Step 1.2.2

Pull terms out from under the radical.

$\frac{10 \sqrt{2}}{3} - \frac{5 \sqrt{2}}{4}$

Step 2

To write $\frac{10 \sqrt{2}}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{10 \sqrt{2}}{3} \cdot \frac{4}{4} - \frac{5 \sqrt{2}}{4}$

Step 3

To write $- \frac{5 \sqrt{2}}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{10 \sqrt{2}}{3} \cdot \frac{4}{4} - \frac{5 \sqrt{2}}{4} \cdot \frac{3}{3}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{10 \sqrt{2}}{3}$ by $\frac{4}{4}$ .

$\frac{10 \sqrt{2} \cdot 4}{3 \cdot 4} - \frac{5 \sqrt{2}}{4} \cdot \frac{3}{3}$

Step 4.2

Multiply $3$ by $4$ .

$\frac{10 \sqrt{2} \cdot 4}{12} - \frac{5 \sqrt{2}}{4} \cdot \frac{3}{3}$

Step 4.3

Multiply $\frac{5 \sqrt{2}}{4}$ by $\frac{3}{3}$ .

$\frac{10 \sqrt{2} \cdot 4}{12} - \frac{5 \sqrt{2} \cdot 3}{4 \cdot 3}$

Step 4.4

Multiply $4$ by $3$ .

$\frac{10 \sqrt{2} \cdot 4}{12} - \frac{5 \sqrt{2} \cdot 3}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{10 \sqrt{2} \cdot 4 - 5 \sqrt{2} \cdot 3}{12}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $4$ by $10$ .

$\frac{40 \sqrt{2} - 5 \sqrt{2} \cdot 3}{12}$

Step 6.2

Multiply $3$ by $- 5$ .

$\frac{40 \sqrt{2} - 15 \sqrt{2}}{12}$

Step 6.3

Subtract $15 \sqrt{2}$ from $40 \sqrt{2}$ .

$\frac{25 \sqrt{2}}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{25 \sqrt{2}}{12}$

Decimal Form:

$2.94627825 \dots$