Simplify 2( square root of 48+ square root of 27)

$2 (\sqrt{48} + \sqrt{27})$

Simplify each term.

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

Factor $16$ out of $48$ .

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

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

$2 (\sqrt{4^{2} \cdot 3} + \sqrt{27})$

$2 (\sqrt{4^{2} \cdot 3} + \sqrt{27})$

Pull terms out from under the radical.

$2 (4 \sqrt{3} + \sqrt{27})$

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

Factor $9$ out of $27$ .

$2 (4 \sqrt{3} + \sqrt{9 (3)})$

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

$2 (4 \sqrt{3} + \sqrt{3^{2} \cdot 3})$

$2 (4 \sqrt{3} + \sqrt{3^{2} \cdot 3})$

Pull terms out from under the radical.

$2 (4 \sqrt{3} + 3 \sqrt{3})$

$2 (4 \sqrt{3} + 3 \sqrt{3})$

Simplify by adding terms.

Add $4 \sqrt{3}$ and $3 \sqrt{3}$ .

$2 (7 \sqrt{3})$

Multiply $7$ by $2$ .

$14 \sqrt{3}$

$14 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$14 \sqrt{3}$

Decimal Form:

$24.24871130 \dots$

Related Questions