Simplify square root of 10z( square root of 10- square root of z)

$\sqrt{10 z} (\sqrt{10} - \sqrt{z})$

Step 1

Apply the distributive property.

$\sqrt{10 z} \sqrt{10} + \sqrt{10 z} (- \sqrt{z})$

Step 2

Multiply $\sqrt{10 z} \sqrt{10}$ .

Combine using the product rule for radicals.

$\sqrt{10 z \cdot 10} + \sqrt{10 z} (- \sqrt{z})$

Multiply $10$ by $10$ .

$\sqrt{100 z} + \sqrt{10 z} (- \sqrt{z})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{100 z} - \sqrt{10 z} \sqrt{z}$

Step 4

Simplify each term.

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} z} - \sqrt{10 z} \sqrt{z}$

Pull terms out from under the radical.

$10 \sqrt{z} - \sqrt{10 z} \sqrt{z}$

Multiply $- \sqrt{10 z} \sqrt{z}$ .

Combine using the product rule for radicals.

$10 \sqrt{z} - \sqrt{z (10 z)}$

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

$10 \sqrt{z} - \sqrt{10 (z^{1} z)}$

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

$10 \sqrt{z} - \sqrt{10 (z^{1} z^{1})}$

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

$10 \sqrt{z} - \sqrt{10 z^{1 + 1}}$

Add $1$ and $1$ .

$10 \sqrt{z} - \sqrt{10 z^{2}}$

Reorder $10$ and $z^{2}$ .

$10 \sqrt{z} - \sqrt{z^{2} \cdot 10}$

Pull terms out from under the radical.

$10 \sqrt{z} - z \sqrt{10}$