Algebra Examples

$\sqrt{16 x^{3} y} - \sqrt{x y} + \sqrt{9 x y^{3}}$

Step 1

Rewrite $16 x^{3} y$ as ${(4 x)}^{2} (x y)$ .

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} x^{3} y} - \sqrt{x y} + \sqrt{9 x y^{3}}$

Step 1.2

Factor out $x^{2}$ .

$\sqrt{4^{2} (x^{2} x) y} - \sqrt{x y} + \sqrt{9 x y^{3}}$

Step 1.3

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$\sqrt{{(4 x)}^{2} x y} - \sqrt{x y} + \sqrt{9 x y^{3}}$

Step 1.4

Add parentheses.

$\sqrt{{(4 x)}^{2} (x y)} - \sqrt{x y} + \sqrt{9 x y^{3}}$

Step 2

Pull terms out from under the radical.

$4 x \sqrt{x y} - \sqrt{x y} + \sqrt{9 x y^{3}}$

Step 3

Rewrite $9 x y^{3}$ as ${(3 y)}^{2} (x y)$ .

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Step 3.1

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

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

Step 3.2

Factor out $y^{2}$ .

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

Step 3.3

Move $x$ .

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

Step 3.4

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

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

Step 3.5

Add parentheses.

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

Step 4

Pull terms out from under the radical.

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