Pre-Algebra Examples

$\frac{\sqrt{63} + 12}{18}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $63$ as $3^{2} \cdot 7$ .

Tap for more steps...

Step 1.1.1

Factor $9$ out of $63$ .

$\frac{\sqrt{9 (7)} + 12}{18}$

Step 1.1.2

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

$\frac{\sqrt{3^{2} \cdot 7} + 12}{18}$

$\frac{\sqrt{3^{2} \cdot 7} + 12}{18}$

Step 1.2

Pull terms out from under the radical.

$\frac{3 \sqrt{7} + 12}{18}$

$\frac{3 \sqrt{7} + 12}{18}$

Step 2

Cancel the common factor of $3 \sqrt{7} + 12$ and $18$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $3 \sqrt{7}$ .

$\frac{3 (\sqrt{7}) + 12}{18}$

Step 2.2

Factor $3$ out of $12$ .

$\frac{3 \sqrt{7} + 3 \cdot 4}{18}$

Step 2.3

Factor $3$ out of $3 \sqrt{7} + 3 \cdot 4$ .

$\frac{3 (\sqrt{7} + 4)}{18}$

Step 2.4

Cancel the common factors.

Tap for more steps...

Step 2.4.1

Factor $3$ out of $18$ .

$\frac{3 (\sqrt{7} + 4)}{3 (6)}$

Step 2.4.2

Cancel the common factor.

$\frac{3 (\sqrt{7} + 4)}{3 \cdot 6}$

Step 2.4.3

Rewrite the expression.

$\frac{\sqrt{7} + 4}{6}$

$\frac{\sqrt{7} + 4}{6}$

$\frac{\sqrt{7} + 4}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{7} + 4}{6}$

Decimal Form:

$1.10762521 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$