Simplify square root of 2x( square root of 2+ square root of x)

$\sqrt{2 x} (\sqrt{2} + \sqrt{x})$

Step 1

Apply the distributive property.

$\sqrt{2 x} \sqrt{2} + \sqrt{2 x} \sqrt{x}$

Step 2

Multiply $\sqrt{2 x} \sqrt{2}$ .

Combine using the product rule for radicals.

$\sqrt{2 x \cdot 2} + \sqrt{2 x} \sqrt{x}$

Multiply $2$ by $2$ .

$\sqrt{4 x} + \sqrt{2 x} \sqrt{x}$

Step 3

Multiply $\sqrt{2 x} \sqrt{x}$ .

Combine using the product rule for radicals.

$\sqrt{4 x} + \sqrt{2 x \cdot x}$

Raise $x$ to the power of $1$ .

$\sqrt{4 x} + \sqrt{2 (x^{1} x)}$

Raise $x$ to the power of $1$ .

$\sqrt{4 x} + \sqrt{2 (x^{1} x^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{4 x} + \sqrt{2 x^{1 + 1}}$

Add $1$ and $1$ .

$\sqrt{4 x} + \sqrt{2 x^{2}}$

Step 4

Simplify each term.

Rewrite $4$ as $2^{2}$ .

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

Pull terms out from under the radical.

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

Reorder $2$ and $x^{2}$ .

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

Pull terms out from under the radical.

$2 \sqrt{x} + x \sqrt{2}$