Simplify square root of 6( square root of 6+x square root of 30)

$\sqrt{6} (\sqrt{6} + x \sqrt{30})$

Step 1

Apply the distributive property.

$\sqrt{6} \sqrt{6} + \sqrt{6} (x \sqrt{30})$

Step 2

Combine using the product rule for radicals.

$\sqrt{6 \cdot 6} + \sqrt{6} (x \sqrt{30})$

Step 3

Multiply $\sqrt{6} (x \sqrt{30})$ .

Combine using the product rule for radicals.

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

Multiply $6$ by $30$ .

$\sqrt{6 \cdot 6} + x \sqrt{180}$

Step 4

Simplify each term.

Multiply $6$ by $6$ .

$\sqrt{36} + x \sqrt{180}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2}} + x \sqrt{180}$

Pull terms out from under the radical, assuming positive real numbers.

$6 + x \sqrt{180}$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$6 + x \sqrt{36 (5)}$

Rewrite $36$ as $6^{2}$ .

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

Pull terms out from under the radical.

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

Move $6$ to the left of $x$ .

$6 + 6 x \sqrt{5}$