Simplify the Radical Expression square root of 5(6+ square root of 2)

$\sqrt{5} (6 + \sqrt{2})$

Apply the distributive property.

$\sqrt{5} \cdot 6 + \sqrt{5} \sqrt{2}$

Move $6$ to the left of $\sqrt{5}$ .

$6 \cdot \sqrt{5} + \sqrt{5} \sqrt{2}$

Combine using the product rule for radicals.

$6 \cdot \sqrt{5} + \sqrt{5 \cdot 2}$

Multiply $5$ by $2$ .

$6 \sqrt{5} + \sqrt{10}$

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{5} + \sqrt{10}$

Decimal Form:

$16.57868552 \dots$