Algebra Examples

$6 \sqrt{18} \div 12 \sqrt{40}$

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 $18$ .

$6 \sqrt{9 (2)} \div 12 \sqrt{40}$

Step 1.1.2

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

$6 \sqrt{3^{2} \cdot 2} \div 12 \sqrt{40}$

Step 1.2

Pull terms out from under the radical.

$6 (| 3 | \sqrt{2}) \div 12 \sqrt{40}$

Step 1.3

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

$6 \cdot 3 \sqrt{2} \div 12 \sqrt{40}$

Step 1.4

Multiply $6$ by $3$ .

$18 \sqrt{2} \div 12 \sqrt{40}$

Step 2

Rewrite the division as a fraction.

$\frac{18 \sqrt{2}}{12} \sqrt{40}$

Step 3

Cancel the common factor of $18$ and $12$ .

Tap for more steps...

Step 3.1

Factor $6$ out of $18 \sqrt{2}$ .

$\frac{6 (3 \sqrt{2})}{12} \sqrt{40}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $6$ out of $12$ .

$\frac{6 (3 \sqrt{2})}{6 (2)} \sqrt{40}$

Step 3.2.2

Cancel the common factor.

$\frac{6 (3 \sqrt{2})}{6 \cdot 2} \sqrt{40}$

Step 3.2.3

Rewrite the expression.

$\frac{3 \sqrt{2}}{2} \sqrt{40}$

Step 4

Rewrite $40$ as $2^{2} \cdot 10$ .

Tap for more steps...

Step 4.1

Factor $4$ out of $40$ .

$\frac{3 \sqrt{2}}{2} \sqrt{4 (10)}$

Step 4.2

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

$\frac{3 \sqrt{2}}{2} \sqrt{2^{2} \cdot 10}$

Step 5

Pull terms out from under the radical.

$\frac{3 \sqrt{2}}{2} (| 2 | \sqrt{10})$

Step 6

Remove non-negative terms from the absolute value.

$\frac{3 \sqrt{2}}{2} (2 \sqrt{10})$

Step 7

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1

Factor $2$ out of $2 \sqrt{10}$ .

$\frac{3 \sqrt{2}}{2} (2 (\sqrt{10}))$

Step 7.2

Cancel the common factor.

$\frac{3 \sqrt{2}}{2} (2 \sqrt{10})$

Step 7.3

Rewrite the expression.

$3 \sqrt{2} \sqrt{10}$

Step 8

Combine using the product rule for radicals.

$3 \sqrt{10 \cdot 2}$

Step 9

Multiply $10$ by $2$ .

$3 \sqrt{20}$

Step 10

Rewrite $20$ as $2^{2} \cdot 5$ .

Tap for more steps...

Step 10.1

Factor $4$ out of $20$ .

$3 \sqrt{4 (5)}$

Step 10.2

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

$3 \sqrt{2^{2} \cdot 5}$

Step 11

Pull terms out from under the radical.

$3 (| 2 | \sqrt{5})$

Step 12

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$3 (2 \sqrt{5})$

Step 13

Multiply $2$ by $3$ .

$6 \sqrt{5}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{5}$

Decimal Form:

$13.41640786 \dots$