Pre-Algebra Examples

$\frac{\sqrt{50}}{3} + \frac{4 \sqrt{2}}{3} - \frac{\sqrt{2}}{\sqrt{9}}$

Step 1

Combine the numerators over the common denominator.

$\frac{\sqrt{50} + 4 \sqrt{2}}{3} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 2

Simplify each term.

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Step 2.1

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

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Step 2.1.1

Factor $25$ out of $50$ .

$\frac{\sqrt{25 (2)} + 4 \sqrt{2}}{3} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 2.1.2

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

$\frac{\sqrt{5^{2} \cdot 2} + 4 \sqrt{2}}{3} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 2.2

Pull terms out from under the radical.

$\frac{5 \sqrt{2} + 4 \sqrt{2}}{3} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 3

Add $5 \sqrt{2}$ and $4 \sqrt{2}$ .

$\frac{9 \sqrt{2}}{3} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $9$ and $3$ .

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Step 4.1.1

Factor $3$ out of $9 \sqrt{2}$ .

$\frac{3 (3 \sqrt{2})}{3} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $3$ out of $3$ .

$\frac{3 (3 \sqrt{2})}{3 (1)} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 4.1.2.2

Cancel the common factor.

$\frac{3 (3 \sqrt{2})}{3 \cdot 1} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 4.1.2.3

Rewrite the expression.

$\frac{3 \sqrt{2}}{1} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 4.1.2.4

Divide $3 \sqrt{2}$ by $1$ .

$3 \sqrt{2} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 4.2

Simplify the denominator.

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Step 4.2.1

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

$3 \sqrt{2} + \frac{- \sqrt{2}}{\sqrt{3^{2}}}$

Step 4.2.2

Pull terms out from under the radical, assuming positive real numbers.

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

Step 4.3

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Combine fractions.

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Step 6.1

Combine $3 \sqrt{2}$ and $\frac{3}{3}$ .

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

Step 6.2

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $3$ by $3$ .

$\frac{9 \sqrt{2} - \sqrt{2}}{3}$

Step 7.2

Subtract $\sqrt{2}$ from $9 \sqrt{2}$ .

$\frac{8 \sqrt{2}}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{8 \sqrt{2}}{3}$

Decimal Form:

$3.77123616 \dots$