Basic Math Examples

$(\sqrt{12 + \sqrt{2}}) (\sqrt{3 + \sqrt{18}})$

Step 1

Combine using the product rule for radicals.

$\sqrt{(12 + \sqrt{2}) (3 + \sqrt{18})}$

Step 2

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 2.1

Factor $9$ out of $18$ .

$\sqrt{(12 + \sqrt{2}) (3 + \sqrt{9 (2)})}$

Step 2.2

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

$\sqrt{(12 + \sqrt{2}) (3 + \sqrt{3^{2} \cdot 2})}$

Step 3

Pull terms out from under the radical.

$\sqrt{(12 + \sqrt{2}) (3 + 3 \sqrt{2})}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{(12 + \sqrt{2}) (3 + 3 \sqrt{2})}$

Decimal Form:

$9.85668955 \dots$