Precalculus Examples

$4 \sqrt{54} - 3 \sqrt{96} + 5 \sqrt{24} - \sqrt{150}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $54$ as $3^{2} \cdot 6$ .

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Step 1.1.1

Factor $9$ out of $54$ .

$4 \sqrt{9 (6)} - 3 \sqrt{96} + 5 \sqrt{24} - \sqrt{150}$

Step 1.1.2

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

$4 \sqrt{3^{2} \cdot 6} - 3 \sqrt{96} + 5 \sqrt{24} - \sqrt{150}$

Step 1.2

Pull terms out from under the radical.

$4 (3 \sqrt{6}) - 3 \sqrt{96} + 5 \sqrt{24} - \sqrt{150}$

Step 1.3

Multiply $3$ by $4$ .

$12 \sqrt{6} - 3 \sqrt{96} + 5 \sqrt{24} - \sqrt{150}$

Step 1.4

Rewrite $96$ as $4^{2} \cdot 6$ .

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Step 1.4.1

Factor $16$ out of $96$ .

$12 \sqrt{6} - 3 \sqrt{16 (6)} + 5 \sqrt{24} - \sqrt{150}$

Step 1.4.2

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

$12 \sqrt{6} - 3 \sqrt{4^{2} \cdot 6} + 5 \sqrt{24} - \sqrt{150}$

Step 1.5

Pull terms out from under the radical.

$12 \sqrt{6} - 3 (4 \sqrt{6}) + 5 \sqrt{24} - \sqrt{150}$

Step 1.6

Multiply $4$ by $- 3$ .

$12 \sqrt{6} - 12 \sqrt{6} + 5 \sqrt{24} - \sqrt{150}$

Step 1.7

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

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Step 1.7.1

Factor $4$ out of $24$ .

$12 \sqrt{6} - 12 \sqrt{6} + 5 \sqrt{4 (6)} - \sqrt{150}$

Step 1.7.2

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

$12 \sqrt{6} - 12 \sqrt{6} + 5 \sqrt{2^{2} \cdot 6} - \sqrt{150}$

Step 1.8

Pull terms out from under the radical.

$12 \sqrt{6} - 12 \sqrt{6} + 5 (2 \sqrt{6}) - \sqrt{150}$

Step 1.9

Multiply $2$ by $5$ .

$12 \sqrt{6} - 12 \sqrt{6} + 10 \sqrt{6} - \sqrt{150}$

Step 1.10

Rewrite $150$ as $5^{2} \cdot 6$ .

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Step 1.10.1

Factor $25$ out of $150$ .

$12 \sqrt{6} - 12 \sqrt{6} + 10 \sqrt{6} - \sqrt{25 (6)}$

Step 1.10.2

Rewrite $25$ as $5^{2}$ .

$12 \sqrt{6} - 12 \sqrt{6} + 10 \sqrt{6} - \sqrt{5^{2} \cdot 6}$

Step 1.11

Pull terms out from under the radical.

$12 \sqrt{6} - 12 \sqrt{6} + 10 \sqrt{6} - (5 \sqrt{6})$

Step 1.12

Multiply $5$ by $- 1$ .

$12 \sqrt{6} - 12 \sqrt{6} + 10 \sqrt{6} - 5 \sqrt{6}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $12 \sqrt{6}$ from $12 \sqrt{6}$ .

$0 + 10 \sqrt{6} - 5 \sqrt{6}$

Step 2.2

Add $0$ and $10 \sqrt{6}$ .

$10 \sqrt{6} - 5 \sqrt{6}$

Step 2.3

Subtract $5 \sqrt{6}$ from $10 \sqrt{6}$ .

$5 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{6}$

Decimal Form:

$12.24744871 \dots$