Trigonometry Examples

$3 \sqrt{\frac{81 x^{5} y^{3}}{3 x^{2}}}$

Step 1

Reduce the expression $\frac{81 x^{5} y^{3}}{3 x^{2}}$ by cancelling the common factors.

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Step 1.1

Factor $3$ out of $81 x^{5} y^{3}$ .

$3 \sqrt{\frac{3 (27 x^{5} y^{3})}{3 x^{2}}}$

Step 1.2

Factor $3$ out of $3 x^{2}$ .

$3 \sqrt{\frac{3 (27 x^{5} y^{3})}{3 (x^{2})}}$

Step 1.3

Cancel the common factor.

$3 \sqrt{\frac{3 (27 x^{5} y^{3})}{3 x^{2}}}$

Step 1.4

Rewrite the expression.

$3 \sqrt{\frac{27 x^{5} y^{3}}{x^{2}}}$

Step 2

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $27 x^{5} y^{3}$ .

$3 \sqrt{\frac{x^{2} (27 x^{3} y^{3})}{x^{2}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$3 \sqrt{\frac{x^{2} (27 x^{3} y^{3})}{x^{2} \cdot 1}}$

Step 2.2.2

Cancel the common factor.

$3 \sqrt{\frac{x^{2} (27 x^{3} y^{3})}{x^{2} \cdot 1}}$

Step 2.2.3

Rewrite the expression.

$3 \sqrt{\frac{27 x^{3} y^{3}}{1}}$

Step 2.2.4

Divide $27 x^{3} y^{3}$ by $1$ .

$3 \sqrt{27 x^{3} y^{3}}$

Step 3

Rewrite $27 x^{3} y^{3}$ as ${(3 x y)}^{2} \cdot (3 x y)$ .

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Step 3.1

Factor $9$ out of $27$ .

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

Step 3.2

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

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

Step 3.3

Factor out $x^{2}$ .

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

Step 3.4

Factor out $y^{2}$ .

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

Step 3.5

Move $x$ .

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

Step 3.6

Move $3$ .

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

Step 3.7

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

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

Step 3.8

Add parentheses.

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

Step 3.9

Add parentheses.

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

Step 4

Pull terms out from under the radical.

$3 (3 x y \sqrt{3 x y})$

Step 5

Multiply $3$ by $3$ .

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