Basic Math Examples

$\frac{7}{9} + \sqrt{8}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $8$ .

$\frac{7}{9} + \sqrt{4 (2)}$

Step 1.1.2

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

$\frac{7}{9} + \sqrt{2^{2} \cdot 2}$

Step 1.2

Pull terms out from under the radical.

$\frac{7}{9} + 2 \sqrt{2}$

Step 2

To write $2 \sqrt{2}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{7}{9} + 2 \sqrt{2} \cdot \frac{9}{9}$

Step 3

Combine $2 \sqrt{2}$ and $\frac{9}{9}$ .

$\frac{7}{9} + \frac{2 \sqrt{2} \cdot 9}{9}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{7 + 2 \sqrt{2} \cdot 9}{9}$

Step 4.2

Multiply $9$ by $2$ .

$\frac{7 + 18 \sqrt{2}}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{7 + 18 \sqrt{2}}{9}$

Decimal Form:

$3.60620490 \dots$