Evaluate square root of 5( square root of 2+4 square root of 2)

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

Step 1

Add $\sqrt{2}$ and $4 \sqrt{2}$ .

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

Step 2

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

Combine using the product rule for radicals.

$5 \sqrt{5 \cdot 2}$

Multiply $5$ by $2$ .

$5 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{10}$

Decimal Form:

$15.81138830 \dots$