Algebra Examples

$10 \sqrt{18} \div 2 \sqrt{9}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $18$ as $3^{2} \cdot 2$ .

Tap for more steps...

Step 1.1.1

Factor $9$ out of $18$ .

$10 \sqrt{9 (2)} \div 2 \sqrt{9}$

Step 1.1.2

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

$10 \sqrt{3^{2} \cdot 2} \div 2 \sqrt{9}$

Step 1.2

Pull terms out from under the radical.

$10 (| 3 | \sqrt{2}) \div 2 \sqrt{9}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$10 \cdot 3 \sqrt{2} \div 2 \sqrt{9}$

Step 1.4

Multiply $10$ by $3$ .

$30 \sqrt{2} \div 2 \sqrt{9}$

Step 2

Rewrite the division as a fraction.

$\frac{30 \sqrt{2}}{2} \sqrt{9}$

Step 3

Cancel the common factor of $30$ and $2$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $30 \sqrt{2}$ .

$\frac{2 (15 \sqrt{2})}{2} \sqrt{9}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $2$ .

$\frac{2 (15 \sqrt{2})}{2 (1)} \sqrt{9}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (15 \sqrt{2})}{2 \cdot 1} \sqrt{9}$

Step 3.2.3

Rewrite the expression.

$\frac{15 \sqrt{2}}{1} \sqrt{9}$

Step 3.2.4

Divide $15 \sqrt{2}$ by $1$ .

$15 \sqrt{2} \sqrt{9}$

Step 4

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

$15 \sqrt{2} \sqrt{3^{2}}$

Step 5

Pull terms out from under the radical.

$15 \sqrt{2} | 3 |$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$15 \sqrt{2} \cdot 3$

Step 7

Multiply $3$ by $15$ .

$45 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$45 \sqrt{2}$

Decimal Form:

$63.63961030 \dots$