Algebra Examples

$2 x \sqrt{20 y^{2}} + 7 y \sqrt{20 x^{2}} - \sqrt{3 x y}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $20$ .

$2 x \sqrt{4 (5) y^{2}} + 7 y \sqrt{20 x^{2}} - \sqrt{3 x y}$

Step 1.1.2

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

$2 x \sqrt{2^{2} \cdot 5 y^{2}} + 7 y \sqrt{20 x^{2}} - \sqrt{3 x y}$

Step 1.1.3

Move $5$ .

$2 x \sqrt{2^{2} y^{2} \cdot 5} + 7 y \sqrt{20 x^{2}} - \sqrt{3 x y}$

Step 1.1.4

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

$2 x \sqrt{{(2 y)}^{2} \cdot 5} + 7 y \sqrt{20 x^{2}} - \sqrt{3 x y}$

Step 1.2

Pull terms out from under the radical.

$2 x (2 y \sqrt{5}) + 7 y \sqrt{20 x^{2}} - \sqrt{3 x y}$

Step 1.3

Multiply $2$ by $2$ .

$4 x (y \sqrt{5}) + 7 y \sqrt{20 x^{2}} - \sqrt{3 x y}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $20$ .

$4 x y \sqrt{5} + 7 y \sqrt{4 (5) x^{2}} - \sqrt{3 x y}$

Step 1.4.2

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

$4 x y \sqrt{5} + 7 y \sqrt{2^{2} \cdot 5 x^{2}} - \sqrt{3 x y}$

Step 1.4.3

Move $5$ .

$4 x y \sqrt{5} + 7 y \sqrt{2^{2} x^{2} \cdot 5} - \sqrt{3 x y}$

Step 1.4.4

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

$4 x y \sqrt{5} + 7 y \sqrt{{(2 x)}^{2} \cdot 5} - \sqrt{3 x y}$

Step 1.5

Pull terms out from under the radical.

$4 x y \sqrt{5} + 7 y (2 x \sqrt{5}) - \sqrt{3 x y}$

Step 1.6

Multiply $2$ by $7$ .

$4 x y \sqrt{5} + 14 y x \sqrt{5} - \sqrt{3 x y}$

Step 2

Add $4 x y \sqrt{5}$ and $14 y x \sqrt{5}$ .

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Step 2.1

Move $y$ .

$4 x y \sqrt{5} + 14 x y \sqrt{5} - \sqrt{3 x y}$

Step 2.2

Add $4 x y \sqrt{5}$ and $14 x y \sqrt{5}$ .

$18 x y \sqrt{5} - \sqrt{3 x y}$