Trigonometry Examples

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

Step 1

Combine $\sqrt{27 y^{2} x}$ and $\sqrt{3 y x}$ into a single radical.

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

Step 2

Reduce the expression $\frac{27 y^{2} x}{3 y x}$ by cancelling the common factors.

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Step 2.1

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

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

Step 2.2

Factor $3$ out of $3 y x$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

$\sqrt{\frac{9 y^{2} x}{y x}}$

Step 3

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

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Step 3.1

Factor $y$ out of $9 y^{2} x$ .

$\sqrt{\frac{y (9 y x)}{y x}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y$ out of $y x$ .

$\sqrt{\frac{y (9 y x)}{y (x)}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{y (9 y x)}{y x}}$

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $9 y$ by $1$ .

$\sqrt{9 y}$

Step 5

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

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

Step 6

Pull terms out from under the radical.

$3 \sqrt{y}$