Algebra Examples

$4 \sqrt{24} - 2 \sqrt{80} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $24$ as $2^{2} \cdot 6$ .

Tap for more steps...

Step 1.1.1

Factor $4$ out of $24$ .

$4 \sqrt{4 (6)} - 2 \sqrt{80} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.1.2

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

$4 \sqrt{2^{2} \cdot 6} - 2 \sqrt{80} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.2

Pull terms out from under the radical.

$4 (| 2 | \sqrt{6}) - 2 \sqrt{80} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.3

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

$4 (2 \sqrt{6}) - 2 \sqrt{80} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.4

Multiply $2$ by $4$ .

$8 \sqrt{6} - 2 \sqrt{80} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.5

Rewrite $80$ as $4^{2} \cdot 5$ .

Tap for more steps...

Step 1.5.1

Factor $16$ out of $80$ .

$8 \sqrt{6} - 2 \sqrt{16 (5)} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.5.2

Rewrite $16$ as $4^{2}$ .

$8 \sqrt{6} - 2 \sqrt{4^{2} \cdot 5} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.6

Pull terms out from under the radical.

$8 \sqrt{6} - 2 (| 4 | \sqrt{5}) + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.7

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

$8 \sqrt{6} - 2 (4 \sqrt{5}) + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.8

Multiply $4$ by $- 2$ .

$8 \sqrt{6} - 8 \sqrt{5} + 11 \sqrt{6} - 3 \sqrt{216}$

Step 1.9

Rewrite $216$ as $6^{2} \cdot 6$ .

Tap for more steps...

Step 1.9.1

Factor $36$ out of $216$ .

$8 \sqrt{6} - 8 \sqrt{5} + 11 \sqrt{6} - 3 \sqrt{36 (6)}$

Step 1.9.2

Rewrite $36$ as $6^{2}$ .

$8 \sqrt{6} - 8 \sqrt{5} + 11 \sqrt{6} - 3 \sqrt{6^{2} \cdot 6}$

Step 1.10

Pull terms out from under the radical.

$8 \sqrt{6} - 8 \sqrt{5} + 11 \sqrt{6} - 3 (| 6 | \sqrt{6})$

Step 1.11

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$8 \sqrt{6} - 8 \sqrt{5} + 11 \sqrt{6} - 3 (6 \sqrt{6})$

Step 1.12

Multiply $6$ by $- 3$ .

$8 \sqrt{6} - 8 \sqrt{5} + 11 \sqrt{6} - 18 \sqrt{6}$

Step 2

Add $8 \sqrt{6}$ and $11 \sqrt{6}$ .

$19 \sqrt{6} - 8 \sqrt{5} - 18 \sqrt{6}$

Step 3

Subtract $18 \sqrt{6}$ from $19 \sqrt{6}$ .

$\sqrt{6} - 8 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{6} - 8 \sqrt{5}$

Decimal Form:

$- 15.43905407 \dots$