Pre-Algebra Examples

$2 \sqrt{27} + 3 \sqrt{16}$

Step 1

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.1

Factor $9$ out of $27$ .

$2 \sqrt{9 (3)} + 3 \sqrt{16}$

Step 1.2

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

$2 \sqrt{3^{2} \cdot 3} + 3 \sqrt{16}$

Step 2

Pull terms out from under the radical.

$2 (3 \sqrt{3}) + 3 \sqrt{16}$

Step 3

Multiply $3$ by $2$ .

$6 \sqrt{3} + 3 \sqrt{16}$

Step 4

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

$6 \sqrt{3} + 3 \sqrt{4^{2}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$6 \sqrt{3} + 3 \cdot 4$

Step 6

Multiply $3$ by $4$ .

$6 \sqrt{3} + 12$

Step 7

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{3} + 12$

Decimal Form:

$22.39230484 \dots$