Simplify Simplify 9 square root of 12+ square root of 32- square root of 72

Simplify $9 \sqrt{12} + \sqrt{32} - \sqrt{72}$

Simplify each term.

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

Factor $4$ out of $12$ .

$9 \sqrt{4 (3)} + \sqrt{32} - \sqrt{72}$

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

$9 \sqrt{2^{2} \cdot 3} + \sqrt{32} - \sqrt{72}$

$9 \sqrt{2^{2} \cdot 3} + \sqrt{32} - \sqrt{72}$

Pull terms out from under the radical.

$9 (2 \sqrt{3}) + \sqrt{32} - \sqrt{72}$

Multiply $2$ by $9$ .

$18 \sqrt{3} + \sqrt{32} - \sqrt{72}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$18 \sqrt{3} + \sqrt{16 (2)} - \sqrt{72}$

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

$18 \sqrt{3} + \sqrt{4^{2} \cdot 2} - \sqrt{72}$

$18 \sqrt{3} + \sqrt{4^{2} \cdot 2} - \sqrt{72}$

Pull terms out from under the radical.

$18 \sqrt{3} + 4 \sqrt{2} - \sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$18 \sqrt{3} + 4 \sqrt{2} - \sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

$18 \sqrt{3} + 4 \sqrt{2} - \sqrt{6^{2} \cdot 2}$

$18 \sqrt{3} + 4 \sqrt{2} - \sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$18 \sqrt{3} + 4 \sqrt{2} - (6 \sqrt{2})$

Multiply $6$ by $- 1$ .

$18 \sqrt{3} + 4 \sqrt{2} - 6 \sqrt{2}$

$18 \sqrt{3} + 4 \sqrt{2} - 6 \sqrt{2}$

Subtract $6 \sqrt{2}$ from $4 \sqrt{2}$ .

$18 \sqrt{3} - 2 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$18 \sqrt{3} - 2 \sqrt{2}$

Decimal Form:

$28.34848741 \dots$

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