Simplify square root of 11( square root of 11+x square root of 33)

$\sqrt{11} (\sqrt{11} + x \sqrt{33})$

Step 1

Apply the distributive property.

$\sqrt{11} \sqrt{11} + \sqrt{11} (x \sqrt{33})$

Step 2

Combine using the product rule for radicals.

$\sqrt{11 \cdot 11} + \sqrt{11} (x \sqrt{33})$

Step 3

Multiply $\sqrt{11} (x \sqrt{33})$ .

Combine using the product rule for radicals.

$\sqrt{11 \cdot 11} + x \sqrt{11 \cdot 33}$

Multiply $11$ by $33$ .

$\sqrt{11 \cdot 11} + x \sqrt{363}$

Step 4

Simplify each term.

Multiply $11$ by $11$ .

$\sqrt{121} + x \sqrt{363}$

Rewrite $121$ as $11^{2}$ .

$\sqrt{11^{2}} + x \sqrt{363}$

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

$11 + x \sqrt{363}$

Rewrite $363$ as $11^{2} \cdot 3$ .

Factor $121$ out of $363$ .

$11 + x \sqrt{121 (3)}$

Rewrite $121$ as $11^{2}$ .

$11 + x \sqrt{11^{2} \cdot 3}$

Pull terms out from under the radical.

$11 + x (11 \sqrt{3})$

Move $11$ to the left of $x$ .

$11 + 11 x \sqrt{3}$