Simplify square root of 20y+ square root of 45y

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

Step 1

Simplify each term.

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

Factor $4$ out of $20$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

Factor $9$ out of $45$ .

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

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

Step 2

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

$5 \sqrt{5 y}$

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