Simplify square root of 48+3 square root of 27-7( square root of 12- square root of 75)

$\sqrt{48} + 3 \sqrt{27} - 7 (\sqrt{12} - \sqrt{75})$

Simplify each term.

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

Factor $16$ out of $48$ .

$\sqrt{16 (3)} + 3 \sqrt{27} - 7 (\sqrt{12} - \sqrt{75})$

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

$\sqrt{4^{2} \cdot 3} + 3 \sqrt{27} - 7 (\sqrt{12} - \sqrt{75})$

Pull terms out from under the radical.

$4 \sqrt{3} + 3 \sqrt{27} - 7 (\sqrt{12} - \sqrt{75})$

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

Factor $9$ out of $27$ .

$4 \sqrt{3} + 3 \sqrt{9 (3)} - 7 (\sqrt{12} - \sqrt{75})$

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

$4 \sqrt{3} + 3 \sqrt{3^{2} \cdot 3} - 7 (\sqrt{12} - \sqrt{75})$

Pull terms out from under the radical.

$4 \sqrt{3} + 3 (3 \sqrt{3}) - 7 (\sqrt{12} - \sqrt{75})$

Multiply $3$ by $3$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (\sqrt{12} - \sqrt{75})$

Simplify each term.

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

Factor $4$ out of $12$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (\sqrt{4 (3)} - \sqrt{75})$

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

$4 \sqrt{3} + 9 \sqrt{3} - 7 (\sqrt{2^{2} \cdot 3} - \sqrt{75})$

Pull terms out from under the radical.

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - \sqrt{75})$

Rewrite $75$ as $5^{2} \cdot 3$ .

Factor $25$ out of $75$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - \sqrt{25 (3)})$

Rewrite $25$ as $5^{2}$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - \sqrt{5^{2} \cdot 3})$

Pull terms out from under the radical.

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - (5 \sqrt{3}))$

Multiply $5$ by $- 1$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (2 \sqrt{3} - 5 \sqrt{3})$

Subtract $5 \sqrt{3}$ from $2 \sqrt{3}$ .

$4 \sqrt{3} + 9 \sqrt{3} - 7 (- 3 \sqrt{3})$

Multiply $- 3$ by $- 7$ .

$4 \sqrt{3} + 9 \sqrt{3} + 21 \sqrt{3}$

Simplify by adding terms.

Add $4 \sqrt{3}$ and $9 \sqrt{3}$ .

$13 \sqrt{3} + 21 \sqrt{3}$

Add $13 \sqrt{3}$ and $21 \sqrt{3}$ .

$34 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$34 \sqrt{3}$

Decimal Form:

$58.88972745 \dots$

Simplify square root of 48+3 square root of 27-7( square root of 12- square root of 75)

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