Evaluate ( square root of 8)/3+(4 square root of 2)/3-( square root of 2)/( square root of 9)

$\frac{\sqrt{8}}{3} + \frac{4 \sqrt{2}}{3} - \frac{\sqrt{2}}{\sqrt{9}}$

Step 1

Combine the numerators over the common denominator.

$\frac{\sqrt{8} + 4 \sqrt{2}}{3} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 2

Simplify each term.

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

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

Step 3

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

$\frac{6 \sqrt{2}}{3} + \frac{- \sqrt{2}}{\sqrt{9}}$

Step 4

Simplify each term.

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 \sqrt{2}$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify the denominator.

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

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

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

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

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Combine fractions.

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

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

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

Multiply $3$ by $2$ .

$\frac{6 \sqrt{2} - \sqrt{2}}{3}$

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

$\frac{5 \sqrt{2}}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5 \sqrt{2}}{3}$

Decimal Form:

$2.35702260 \dots$

Evaluate ( square root of 8)/3+(4 square root of 2)/3-( square root of 2)/( square root of 9)

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