Simplify square root of 50y- square root of 8y

$\sqrt{50 y} - \sqrt{8 y}$

Step 1

Simplify each term.

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

Factor $25$ out of $50$ .

$\sqrt{25 (2) y} - \sqrt{8 y}$

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

$\sqrt{5^{2} \cdot 2 y} - \sqrt{8 y}$

Add parentheses.

$\sqrt{5^{2} \cdot (2 y)} - \sqrt{8 y}$

$\sqrt{5^{2} \cdot (2 y)} - \sqrt{8 y}$

Pull terms out from under the radical.

$5 \sqrt{2 y} - \sqrt{8 y}$

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

Factor $4$ out of $8$ .

$5 \sqrt{2 y} - \sqrt{4 (2) y}$

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

$5 \sqrt{2 y} - \sqrt{2^{2} \cdot 2 y}$

Add parentheses.

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

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

Pull terms out from under the radical.

$5 \sqrt{2 y} - (2 \sqrt{2 y})$

Multiply $2$ by $- 1$ .

$5 \sqrt{2 y} - 2 \sqrt{2 y}$

$5 \sqrt{2 y} - 2 \sqrt{2 y}$

Step 2

Subtract $2 \sqrt{2 y}$ from $5 \sqrt{2 y}$ .

$3 \sqrt{2 y}$

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