Evaluate square root of 6( square root of 5+ square root of 11)

$\sqrt{6} (\sqrt{5} + \sqrt{11})$

Step 1

Simplify terms.

Apply the distributive property.

$\sqrt{6} \sqrt{5} + \sqrt{6} \sqrt{11}$

Combine using the product rule for radicals.

$\sqrt{6 \cdot 5} + \sqrt{6} \sqrt{11}$

Combine using the product rule for radicals.

$\sqrt{6 \cdot 5} + \sqrt{6 \cdot 11}$

Step 2

Simplify each term.

Multiply $6$ by $5$ .

$\sqrt{30} + \sqrt{6 \cdot 11}$

Multiply $6$ by $11$ .

$\sqrt{30} + \sqrt{66}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{30} + \sqrt{66}$

Decimal Form:

$13.60126397 \dots$