Simplify 2 square root of 72-3 square root of 32

$2 \sqrt{72} - 3 \sqrt{32}$

Step 1

Simplify each term.

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

Factor $36$ out of $72$ .

$2 \sqrt{36 (2)} - 3 \sqrt{32}$

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

$2 \sqrt{6^{2} \cdot 2} - 3 \sqrt{32}$

$2 \sqrt{6^{2} \cdot 2} - 3 \sqrt{32}$

Pull terms out from under the radical.

$2 (6 \sqrt{2}) - 3 \sqrt{32}$

Multiply $6$ by $2$ .

$12 \sqrt{2} - 3 \sqrt{32}$

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

Factor $16$ out of $32$ .

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

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

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

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

Pull terms out from under the radical.

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

Multiply $4$ by $- 3$ .

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

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

Step 2

Subtract $12 \sqrt{2}$ from $12 \sqrt{2}$ .

$0$

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