Basic Math Examples

$\sqrt{50 y} - 9 \sqrt{2 y} + \sqrt{72 y}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $25$ out of $50$ .

$\sqrt{25 (2) y} - 9 \sqrt{2 y} + \sqrt{72 y}$

Step 1.1.2

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

$\sqrt{5^{2} \cdot 2 y} - 9 \sqrt{2 y} + \sqrt{72 y}$

Step 1.1.3

Add parentheses.

$\sqrt{5^{2} \cdot (2 y)} - 9 \sqrt{2 y} + \sqrt{72 y}$

Step 1.2

Pull terms out from under the radical.

$5 \sqrt{2 y} - 9 \sqrt{2 y} + \sqrt{72 y}$

Step 1.3

Rewrite $72 y$ as $6^{2} \cdot (2 y)$ .

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Step 1.3.1

Factor $36$ out of $72$ .

$5 \sqrt{2 y} - 9 \sqrt{2 y} + \sqrt{36 (2) y}$

Step 1.3.2

Rewrite $36$ as $6^{2}$ .

$5 \sqrt{2 y} - 9 \sqrt{2 y} + \sqrt{6^{2} \cdot 2 y}$

Step 1.3.3

Add parentheses.

$5 \sqrt{2 y} - 9 \sqrt{2 y} + \sqrt{6^{2} \cdot (2 y)}$

Step 1.4

Pull terms out from under the radical.

$5 \sqrt{2 y} - 9 \sqrt{2 y} + 6 \sqrt{2 y}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $9 \sqrt{2 y}$ from $5 \sqrt{2 y}$ .

$- 4 \sqrt{2 y} + 6 \sqrt{2 y}$

Step 2.2

Add $- 4 \sqrt{2 y}$ and $6 \sqrt{2 y}$ .

$2 \sqrt{2 y}$