Evaluate 5 square root of 48-2 square root of 12

$5 \sqrt{48} - 2 \sqrt{12}$

Step 1

Simplify each term.

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

Factor $16$ out of $48$ .

$5 \sqrt{16 (3)} - 2 \sqrt{12}$

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

$5 \sqrt{4^{2} \cdot 3} - 2 \sqrt{12}$

$5 \sqrt{4^{2} \cdot 3} - 2 \sqrt{12}$

Pull terms out from under the radical.

$5 (4 \sqrt{3}) - 2 \sqrt{12}$

Multiply $4$ by $5$ .

$20 \sqrt{3} - 2 \sqrt{12}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$20 \sqrt{3} - 2 \sqrt{4 (3)}$

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

$20 \sqrt{3} - 2 \sqrt{2^{2} \cdot 3}$

$20 \sqrt{3} - 2 \sqrt{2^{2} \cdot 3}$

Pull terms out from under the radical.

$20 \sqrt{3} - 2 (2 \sqrt{3})$

Multiply $2$ by $- 2$ .

$20 \sqrt{3} - 4 \sqrt{3}$

$20 \sqrt{3} - 4 \sqrt{3}$

Step 2

Subtract $4 \sqrt{3}$ from $20 \sqrt{3}$ .

$16 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$16 \sqrt{3}$

Decimal Form:

$27.71281292 \dots$

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