Pre-Algebra Examples

$\frac{\sqrt{48 x^{3} y}}{3 x y}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $48 x^{3} y$ as ${(4 x)}^{2} \cdot (3 x y)$ .

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Step 1.1.1

Factor $16$ out of $48$ .

$\frac{\sqrt{16 (3) x^{3} y}}{3 x y}$

Step 1.1.2

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

$\frac{\sqrt{4^{2} \cdot 3 x^{3} y}}{3 x y}$

Step 1.1.3

Factor out $x^{2}$ .

$\frac{\sqrt{4^{2} \cdot 3 (x^{2} x) y}}{3 x y}$

Step 1.1.4

Move $3$ .

$\frac{\sqrt{4^{2} x^{2} \cdot 3 x y}}{3 x y}$

Step 1.1.5

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

$\frac{\sqrt{{(4 x)}^{2} \cdot 3 x y}}{3 x y}$

Step 1.1.6

Add parentheses.

$\frac{\sqrt{{(4 x)}^{2} \cdot 3 (x y)}}{3 x y}$

Step 1.1.7

Add parentheses.

$\frac{\sqrt{{(4 x)}^{2} \cdot (3 x y)}}{3 x y}$

$\frac{\sqrt{{(4 x)}^{2} \cdot (3 x y)}}{3 x y}$

Step 1.2

Pull terms out from under the radical.

$\frac{4 x \sqrt{3 x y}}{3 x y}$

$\frac{4 x \sqrt{3 x y}}{3 x y}$

Step 2

Cancel the common factor of $x$ .

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Step 2.1

Cancel the common factor.

$\frac{4 x \sqrt{3 x y}}{3 x y}$

Step 2.2

Rewrite the expression.

$\frac{4 \sqrt{3 x y}}{3 y}$

$\frac{4 \sqrt{3 x y}}{3 y}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$