Simplify square root of 3( square root of 72-3 square root of 2)

$\sqrt{3} (\sqrt{72} - 3 \sqrt{2})$

Step 1

Simplify each term.

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

Factor $36$ out of $72$ .

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

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

$\sqrt{3} (\sqrt{6^{2} \cdot 2} - 3 \sqrt{2})$

$\sqrt{3} (\sqrt{6^{2} \cdot 2} - 3 \sqrt{2})$

Pull terms out from under the radical.

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

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

Step 2

Subtract $3 \sqrt{2}$ from $6 \sqrt{2}$ .

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

Step 3

Multiply $\sqrt{3} (3 \sqrt{2})$ .

Combine using the product rule for radicals.

$3 \sqrt{3 \cdot 2}$

Multiply $3$ by $2$ .

$3 \sqrt{6}$

$3 \sqrt{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{6}$

Decimal Form:

$7.34846922 \dots$

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