Simplify square root of 2z( square root of 2- square root of z)

$\sqrt{2 z} (\sqrt{2} - \sqrt{z})$

Step 1

Apply the distributive property.

$\sqrt{2 z} \sqrt{2} + \sqrt{2 z} (- \sqrt{z})$

Step 2

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

Combine using the product rule for radicals.

$\sqrt{2 z \cdot 2} + \sqrt{2 z} (- \sqrt{z})$

Multiply $2$ by $2$ .

$\sqrt{4 z} + \sqrt{2 z} (- \sqrt{z})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{4 z} - \sqrt{2 z} \sqrt{z}$

Step 4

Simplify each term.

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

$\sqrt{2^{2} z} - \sqrt{2 z} \sqrt{z}$

Pull terms out from under the radical.

$2 \sqrt{z} - \sqrt{2 z} \sqrt{z}$

Multiply $- \sqrt{2 z} \sqrt{z}$ .

Combine using the product rule for radicals.

$2 \sqrt{z} - \sqrt{z (2 z)}$

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

$2 \sqrt{z} - \sqrt{2 (z^{1} z)}$

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

$2 \sqrt{z} - \sqrt{2 (z^{1} z^{1})}$

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

$2 \sqrt{z} - \sqrt{2 z^{1 + 1}}$

Add $1$ and $1$ .

$2 \sqrt{z} - \sqrt{2 z^{2}}$

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

$2 \sqrt{z} - \sqrt{z^{2} \cdot 2}$

Pull terms out from under the radical.

$2 \sqrt{z} - z \sqrt{2}$