Evaluate 2 square root of 27-3 square root of 48

$2 \sqrt{27} - 3 \sqrt{48}$

Step 1

Simplify each term.

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

Factor $9$ out of $27$ .

$2 \sqrt{9 (3)} - 3 \sqrt{48}$

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

$2 \sqrt{3^{2} \cdot 3} - 3 \sqrt{48}$

$2 \sqrt{3^{2} \cdot 3} - 3 \sqrt{48}$

Pull terms out from under the radical.

$2 (3 \sqrt{3}) - 3 \sqrt{48}$

Multiply $3$ by $2$ .

$6 \sqrt{3} - 3 \sqrt{48}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$6 \sqrt{3} - 3 \sqrt{16 (3)}$

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

$6 \sqrt{3} - 3 \sqrt{4^{2} \cdot 3}$

$6 \sqrt{3} - 3 \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

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

Multiply $4$ by $- 3$ .

$6 \sqrt{3} - 12 \sqrt{3}$

$6 \sqrt{3} - 12 \sqrt{3}$

Step 2

Subtract $12 \sqrt{3}$ from $6 \sqrt{3}$ .

$- 6 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 6 \sqrt{3}$

Decimal Form:

$- 10.39230484 \dots$

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