Trigonometry Examples

$\frac{\sqrt{100 x^{4} y^{2}}}{2 \sqrt{25 x^{2} y}}$

Step 1

Combine $\sqrt{100 x^{4} y^{2}}$ and $\sqrt{25 x^{2} y}$ into a single radical.

$\frac{\sqrt{\frac{100 x^{4} y^{2}}{25 x^{2} y}}}{2}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $100$ and $25$ .

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Step 2.1.1

Factor $25$ out of $100 x^{4} y^{2}$ .

$\frac{\sqrt{\frac{25 (4 x^{4} y^{2})}{25 x^{2} y}}}{2}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $25$ out of $25 x^{2} y$ .

$\frac{\sqrt{\frac{25 (4 x^{4} y^{2})}{25 (x^{2} y)}}}{2}$

Step 2.1.2.2

Cancel the common factor.

$\frac{\sqrt{\frac{25 (4 x^{4} y^{2})}{25 (x^{2} y)}}}{2}$

Step 2.1.2.3

Rewrite the expression.

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

Step 2.2

Cancel the common factor of $x^{4}$ and $x^{2}$ .

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Step 2.2.1

Factor $x^{2}$ out of $4 x^{4} y^{2}$ .

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

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

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

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

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

Step 2.3

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

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Step 2.3.1

Factor $y$ out of $4 x^{2} y^{2}$ .

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

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Raise $y$ to the power of $1$ .

$\frac{\sqrt{\frac{y (4 x^{2} y)}{y^{1}}}}{2}$

Step 2.3.2.2

Factor $y$ out of $y^{1}$ .

$\frac{\sqrt{\frac{y (4 x^{2} y)}{y \cdot 1}}}{2}$

Step 2.3.2.3

Cancel the common factor.

$\frac{\sqrt{\frac{y (4 x^{2} y)}{y \cdot 1}}}{2}$

Step 2.3.2.4

Rewrite the expression.

$\frac{\sqrt{\frac{4 x^{2} y}{1}}}{2}$

Step 2.3.2.5

Divide $4 x^{2} y$ by $1$ .

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

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

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

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

Step 3.2

Pull terms out from under the radical.

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $x \sqrt{y}$ by $1$ .

$x \sqrt{y}$