Simplify square root of 2( square root of 45+ square root of 5)

$\sqrt{2} (\sqrt{45} + \sqrt{5})$

Step 1

Simplify each term.

Rewrite $45$ as $3^{2} \cdot 5$ .

Factor $9$ out of $45$ .

$\sqrt{2} (\sqrt{9 (5)} + \sqrt{5})$

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

$\sqrt{2} (\sqrt{3^{2} \cdot 5} + \sqrt{5})$

$\sqrt{2} (\sqrt{3^{2} \cdot 5} + \sqrt{5})$

Pull terms out from under the radical.

$\sqrt{2} (3 \sqrt{5} + \sqrt{5})$

$\sqrt{2} (3 \sqrt{5} + \sqrt{5})$

Step 2

Add $3 \sqrt{5}$ and $\sqrt{5}$ .

$\sqrt{2} (4 \sqrt{5})$

Step 3

Multiply $\sqrt{2} (4 \sqrt{5})$ .

Combine using the product rule for radicals.

$4 \sqrt{2 \cdot 5}$

Multiply $2$ by $5$ .

$4 \sqrt{10}$

$4 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{10}$

Decimal Form:

$12.64911064 \dots$

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