Simplify square root of 20z+ square root of 45z

$\sqrt{20 z} + \sqrt{45 z}$

Step 1

Simplify each term.

Rewrite $20 z$ as $2^{2} \cdot (5 z)$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5) z} + \sqrt{45 z}$

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

$\sqrt{2^{2} \cdot 5 z} + \sqrt{45 z}$

Add parentheses.

$\sqrt{2^{2} \cdot (5 z)} + \sqrt{45 z}$

$\sqrt{2^{2} \cdot (5 z)} + \sqrt{45 z}$

Pull terms out from under the radical.

$2 \sqrt{5 z} + \sqrt{45 z}$

Rewrite $45 z$ as $3^{2} \cdot (5 z)$ .

Factor $9$ out of $45$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

Step 2

Add $2 \sqrt{5 z}$ and $3 \sqrt{5 z}$ .

$5 \sqrt{5 z}$

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