Simplify square root of 50z- square root of 18z

$\sqrt{50 z} - \sqrt{18 z}$

Step 1

Simplify each term.

Rewrite $50 z$ as $5^{2} \cdot (2 z)$ .

Factor $25$ out of $50$ .

$\sqrt{25 (2) z} - \sqrt{18 z}$

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

$\sqrt{5^{2} \cdot 2 z} - \sqrt{18 z}$

Add parentheses.

$\sqrt{5^{2} \cdot (2 z)} - \sqrt{18 z}$

$\sqrt{5^{2} \cdot (2 z)} - \sqrt{18 z}$

Pull terms out from under the radical.

$5 \sqrt{2 z} - \sqrt{18 z}$

Rewrite $18 z$ as $3^{2} \cdot (2 z)$ .

Factor $9$ out of $18$ .

$5 \sqrt{2 z} - \sqrt{9 (2) z}$

Rewrite $9$ as $3^{2}$ .

$5 \sqrt{2 z} - \sqrt{3^{2} \cdot 2 z}$

Add parentheses.

$5 \sqrt{2 z} - \sqrt{3^{2} \cdot (2 z)}$

$5 \sqrt{2 z} - \sqrt{3^{2} \cdot (2 z)}$

Pull terms out from under the radical.

$5 \sqrt{2 z} - (3 \sqrt{2 z})$

Multiply $3$ by $- 1$ .

$5 \sqrt{2 z} - 3 \sqrt{2 z}$

$5 \sqrt{2 z} - 3 \sqrt{2 z}$

Step 2

Subtract $3 \sqrt{2 z}$ from $5 \sqrt{2 z}$ .

$2 \sqrt{2 z}$

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