Simplify square root of 18y+ square root of 8y

$\sqrt{18 y} + \sqrt{8 y}$

Step 1

Simplify each term.

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

Factor $9$ out of $18$ .

$\sqrt{9 (2) y} + \sqrt{8 y}$

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

$\sqrt{3^{2} \cdot 2 y} + \sqrt{8 y}$

Add parentheses.

$\sqrt{3^{2} \cdot (2 y)} + \sqrt{8 y}$

$\sqrt{3^{2} \cdot (2 y)} + \sqrt{8 y}$

Pull terms out from under the radical.

$3 \sqrt{2 y} + \sqrt{8 y}$

Rewrite $8 y$ as $2^{2} \cdot (2 y)$ .

Factor $4$ out of $8$ .

$3 \sqrt{2 y} + \sqrt{4 (2) y}$

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

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

Add parentheses.

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

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

Pull terms out from under the radical.

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

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

Step 2

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

$5 \sqrt{2 y}$

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