Pre-Algebra Examples

$\sqrt{2 - 7 (- \frac{1}{9}) + 5}$

Step 1

Multiply $- 7 (- \frac{1}{9})$ .

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Step 1.1

Multiply $- 1$ by $- 7$ .

$\sqrt{2 + 7 (\frac{1}{9}) + 5}$

Step 1.2

Combine $7$ and $\frac{1}{9}$ .

$\sqrt{2 + \frac{7}{9} + 5}$

Step 2

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

$\sqrt{2 \cdot \frac{9}{9} + \frac{7}{9} + 5}$

Step 3

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

$\sqrt{\frac{2 \cdot 9}{9} + \frac{7}{9} + 5}$

Step 4

Combine the numerators over the common denominator.

$\sqrt{\frac{2 \cdot 9 + 7}{9} + 5}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $9$ .

$\sqrt{\frac{18 + 7}{9} + 5}$

Step 5.2

Add $18$ and $7$ .

$\sqrt{\frac{25}{9} + 5}$

Step 6

To write $5$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\sqrt{\frac{25}{9} + 5 \cdot \frac{9}{9}}$

Step 7

Combine $5$ and $\frac{9}{9}$ .

$\sqrt{\frac{25}{9} + \frac{5 \cdot 9}{9}}$

Step 8

Combine the numerators over the common denominator.

$\sqrt{\frac{25 + 5 \cdot 9}{9}}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $5$ by $9$ .

$\sqrt{\frac{25 + 45}{9}}$

Step 9.2

Add $25$ and $45$ .

$\sqrt{\frac{70}{9}}$

Step 10

Rewrite $\sqrt{\frac{70}{9}}$ as $\frac{\sqrt{70}}{\sqrt{9}}$ .

$\frac{\sqrt{70}}{\sqrt{9}}$

Step 11

Simplify the denominator.

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Step 11.1

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

$\frac{\sqrt{70}}{\sqrt{3^{2}}}$

Step 11.2

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

$\frac{\sqrt{70}}{3}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{70}}{3}$

Decimal Form:

$2.78886675 \dots$