Simplify square root of 5z( square root of 5- square root of z)

$\sqrt{5 z} (\sqrt{5} - \sqrt{z})$

Step 1

Apply the distributive property.

$\sqrt{5 z} \sqrt{5} + \sqrt{5 z} (- \sqrt{z})$

Step 2

Multiply $\sqrt{5 z} \sqrt{5}$ .

Combine using the product rule for radicals.

$\sqrt{5 z \cdot 5} + \sqrt{5 z} (- \sqrt{z})$

Multiply $5$ by $5$ .

$\sqrt{25 z} + \sqrt{5 z} (- \sqrt{z})$

Step 3

Rewrite using the commutative property of multiplication.

$\sqrt{25 z} - \sqrt{5 z} \sqrt{z}$

Step 4

Simplify each term.

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} z} - \sqrt{5 z} \sqrt{z}$

Pull terms out from under the radical.

$5 \sqrt{z} - \sqrt{5 z} \sqrt{z}$

Multiply $- \sqrt{5 z} \sqrt{z}$ .

Combine using the product rule for radicals.

$5 \sqrt{z} - \sqrt{z (5 z)}$

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

$5 \sqrt{z} - \sqrt{5 (z^{1} z)}$

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

$5 \sqrt{z} - \sqrt{5 (z^{1} z^{1})}$

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

$5 \sqrt{z} - \sqrt{5 z^{1 + 1}}$

Add $1$ and $1$ .

$5 \sqrt{z} - \sqrt{5 z^{2}}$

Reorder $5$ and $z^{2}$ .

$5 \sqrt{z} - \sqrt{z^{2} \cdot 5}$

Pull terms out from under the radical.

$5 \sqrt{z} - z \sqrt{5}$