Algebra Examples

$\sqrt{24} + \sqrt{54}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $24$ .

$\sqrt{4 (6)} + \sqrt{54}$

Step 1.1.2

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

$\sqrt{2^{2} \cdot 6} + \sqrt{54}$

Step 1.2

Pull terms out from under the radical.

$| 2 | \sqrt{6} + \sqrt{54}$

Step 1.3

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

$2 \sqrt{6} + \sqrt{54}$

Step 1.4

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

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Step 1.4.1

Factor $9$ out of $54$ .

$2 \sqrt{6} + \sqrt{9 (6)}$

Step 1.4.2

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

$2 \sqrt{6} + \sqrt{3^{2} \cdot 6}$

Step 1.5

Pull terms out from under the radical.

$2 \sqrt{6} + | 3 | \sqrt{6}$

Step 1.6

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

$2 \sqrt{6} + 3 \sqrt{6}$

Step 2

Add $2 \sqrt{6}$ and $3 \sqrt{6}$ .

$5 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{6}$

Decimal Form:

$12.24744871 \dots$