Evaluate square root of 54+ square root of 24

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

Step 1

Simplify each term.

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

Factor $9$ out of $54$ .

$\sqrt{9 (6)} + \sqrt{24}$

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

$\sqrt{3^{2} \cdot 6} + \sqrt{24}$

$\sqrt{3^{2} \cdot 6} + \sqrt{24}$

Pull terms out from under the radical.

$3 \sqrt{6} + \sqrt{24}$

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

Factor $4$ out of $24$ .

$3 \sqrt{6} + \sqrt{4 (6)}$

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

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

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

Pull terms out from under the radical.

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

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

Step 2

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

$5 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{6}$

Decimal Form:

$12.24744871 \dots$

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