Trigonometry Examples

$\sqrt{18 x y^{3}}$

Step 1

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

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Step 1.1

Factor $9$ out of $18$ .

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

Step 1.2

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

$\sqrt{3^{2} \cdot 2 x y^{3}}$

Step 1.3

Factor out $y^{2}$ .

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

Step 1.4

Move $x$ .

$\sqrt{3^{2} \cdot 2 y^{2} x y}$

Step 1.5

Move $2$ .

$\sqrt{3^{2} y^{2} \cdot 2 x y}$

Step 1.6

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

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

Step 1.7

Add parentheses.

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

Step 1.8

Add parentheses.

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

Step 2

Pull terms out from under the radical.

$3 y \sqrt{2 x y}$