Calculus Examples

$\sqrt{24 x^{3} y^{9}}$

Step 1

Rewrite $24 x^{3} y^{9}$ as ${(2 x y^{4})}^{2} \cdot (6 x y)$ .

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Step 1.1

Factor $4$ out of $24$ .

$\sqrt{4 (6) x^{3} y^{9}}$

Step 1.2

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

$\sqrt{2^{2} \cdot 6 x^{3} y^{9}}$

Step 1.3

Factor out $x^{2}$ .

$\sqrt{2^{2} \cdot 6 (x^{2} x) y^{9}}$

Step 1.4

Factor out $y^{8}$ .

$\sqrt{2^{2} \cdot 6 (x^{2} x) (y^{8} y)}$

Step 1.5

Rewrite $y^{8}$ as ${(y^{4})}^{2}$ .

$\sqrt{2^{2} \cdot 6 (x^{2} x) ({(y^{4})}^{2} y)}$

Step 1.6

Move $x$ .

$\sqrt{2^{2} \cdot 6 (x^{2}) {(y^{4})}^{2} x y}$

Step 1.7

Move $6$ .

$\sqrt{2^{2} (x^{2}) {(y^{4})}^{2} \cdot 6 x y}$

Step 1.8

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

$\sqrt{{(2 x y^{4})}^{2} \cdot 6 x y}$

Step 1.9

Add parentheses.

$\sqrt{{(2 x y^{4})}^{2} \cdot 6 (x y)}$

Step 1.10

Add parentheses.

$\sqrt{{(2 x y^{4})}^{2} \cdot (6 x y)}$

Step 2

Pull terms out from under the radical.

$2 x y^{4} \sqrt{6 x y}$