Algebra Examples

$\sqrt{18 x^{2} y} + \sqrt{8 x^{2} y} - \sqrt{50 x^{2} y}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $18$ .

$\sqrt{9 (2) x^{2} y} + \sqrt{8 x^{2} y} - \sqrt{50 x^{2} y}$

Step 1.1.2

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

$\sqrt{3^{2} \cdot 2 x^{2} y} + \sqrt{8 x^{2} y} - \sqrt{50 x^{2} y}$

Step 1.1.3

Move $2$ .

$\sqrt{3^{2} x^{2} \cdot 2 y} + \sqrt{8 x^{2} y} - \sqrt{50 x^{2} y}$

Step 1.1.4

Rewrite $3^{2} x^{2}$ as ${(3 x)}^{2}$ .

$\sqrt{{(3 x)}^{2} \cdot 2 y} + \sqrt{8 x^{2} y} - \sqrt{50 x^{2} y}$

Step 1.1.5

Add parentheses.

$\sqrt{{(3 x)}^{2} \cdot (2 y)} + \sqrt{8 x^{2} y} - \sqrt{50 x^{2} y}$

Step 1.2

Pull terms out from under the radical.

$3 x \sqrt{2 y} + \sqrt{8 x^{2} y} - \sqrt{50 x^{2} y}$

Step 1.3

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

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Step 1.3.1

Factor $4$ out of $8$ .

$3 x \sqrt{2 y} + \sqrt{4 (2) x^{2} y} - \sqrt{50 x^{2} y}$

Step 1.3.2

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

$3 x \sqrt{2 y} + \sqrt{2^{2} \cdot 2 x^{2} y} - \sqrt{50 x^{2} y}$

Step 1.3.3

Move $2$ .

$3 x \sqrt{2 y} + \sqrt{2^{2} x^{2} \cdot 2 y} - \sqrt{50 x^{2} y}$

Step 1.3.4

Rewrite $2^{2} x^{2}$ as ${(2 x)}^{2}$ .

$3 x \sqrt{2 y} + \sqrt{{(2 x)}^{2} \cdot 2 y} - \sqrt{50 x^{2} y}$

Step 1.3.5

Add parentheses.

$3 x \sqrt{2 y} + \sqrt{{(2 x)}^{2} \cdot (2 y)} - \sqrt{50 x^{2} y}$

Step 1.4

Pull terms out from under the radical.

$3 x \sqrt{2 y} + 2 x \sqrt{2 y} - \sqrt{50 x^{2} y}$

Step 1.5

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

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Step 1.5.1

Factor $25$ out of $50$ .

$3 x \sqrt{2 y} + 2 x \sqrt{2 y} - \sqrt{25 (2) x^{2} y}$

Step 1.5.2

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

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

Step 1.5.3

Move $2$ .

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

Step 1.5.4

Rewrite $5^{2} x^{2}$ as ${(5 x)}^{2}$ .

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

Step 1.5.5

Add parentheses.

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

Step 1.6

Pull terms out from under the radical.

$3 x \sqrt{2 y} + 2 x \sqrt{2 y} - (5 x \sqrt{2 y})$

Step 1.7

Multiply $5$ by $- 1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

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

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

Step 2.2

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

$0$