Evaluate square root of 6( square root of 11+ square root of 7)

$\sqrt{6} (\sqrt{11} + \sqrt{7})$

Step 1

Simplify terms.

Apply the distributive property.

$\sqrt{6} \sqrt{11} + \sqrt{6} \sqrt{7}$

Combine using the product rule for radicals.

$\sqrt{6 \cdot 11} + \sqrt{6} \sqrt{7}$

Combine using the product rule for radicals.

$\sqrt{6 \cdot 11} + \sqrt{6 \cdot 7}$

Step 2

Simplify each term.

Multiply $6$ by $11$ .

$\sqrt{66} + \sqrt{6 \cdot 7}$

Multiply $6$ by $7$ .

$\sqrt{66} + \sqrt{42}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{66} + \sqrt{42}$

Decimal Form:

$14.60477910 \dots$