Evaluate 2 square root of 6+3 square root of 54

$2 \sqrt{6} + 3 \sqrt{54}$

Step 1

Simplify each term.

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

Factor $9$ out of $54$ .

$2 \sqrt{6} + 3 \sqrt{9 (6)}$

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $3$ .

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

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

Step 2

Add $2 \sqrt{6}$ and $9 \sqrt{6}$ .

$11 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$11 \sqrt{6}$

Decimal Form:

$26.94438717 \dots$

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