Simplify square root of 10( square root of 10+z square root of 30)

$\sqrt{10} (\sqrt{10} + z \sqrt{30})$

Step 1

Apply the distributive property.

$\sqrt{10} \sqrt{10} + \sqrt{10} (z \sqrt{30})$

Step 2

Combine using the product rule for radicals.

$\sqrt{10 \cdot 10} + \sqrt{10} (z \sqrt{30})$

Step 3

Multiply $\sqrt{10} (z \sqrt{30})$ .

Combine using the product rule for radicals.

$\sqrt{10 \cdot 10} + z \sqrt{10 \cdot 30}$

Multiply $10$ by $30$ .

$\sqrt{10 \cdot 10} + z \sqrt{300}$

Step 4

Simplify each term.

Multiply $10$ by $10$ .

$\sqrt{100} + z \sqrt{300}$

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

$\sqrt{10^{2}} + z \sqrt{300}$

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

$10 + z \sqrt{300}$

Rewrite $300$ as $10^{2} \cdot 3$ .

Factor $100$ out of $300$ .

$10 + z \sqrt{100 (3)}$

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

$10 + z \sqrt{10^{2} \cdot 3}$

Pull terms out from under the radical.

$10 + z (10 \sqrt{3})$

Move $10$ to the left of $z$ .

$10 + 10 z \sqrt{3}$