Trigonometry Examples

$\sqrt{\frac{98 x^{4} y^{2}}{2 x y}}$

Step 1

Reduce the expression $\frac{98 x^{4} y^{2}}{2 x y}$ by cancelling the common factors.

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Step 1.1

Factor $2$ out of $98 x^{4} y^{2}$ .

$\sqrt{\frac{2 (49 x^{4} y^{2})}{2 x y}}$

Step 1.2

Factor $2$ out of $2 x y$ .

$\sqrt{\frac{2 (49 x^{4} y^{2})}{2 (x y)}}$

Step 1.3

Cancel the common factor.

$\sqrt{\frac{2 (49 x^{4} y^{2})}{2 (x y)}}$

Step 1.4

Rewrite the expression.

$\sqrt{\frac{49 x^{4} y^{2}}{x y}}$

$\sqrt{\frac{49 x^{4} y^{2}}{x y}}$

Step 2

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

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Step 2.1

Factor $x$ out of $49 x^{4} y^{2}$ .

$\sqrt{\frac{x (49 x^{3} y^{2})}{x y}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x$ out of $x y$ .

$\sqrt{\frac{x (49 x^{3} y^{2})}{x (y)}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{x (49 x^{3} y^{2})}{x y}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{49 x^{3} y^{2}}{y}}$

$\sqrt{\frac{49 x^{3} y^{2}}{y}}$

$\sqrt{\frac{49 x^{3} y^{2}}{y}}$

Step 3

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

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Step 3.1

Factor $y$ out of $49 x^{3} y^{2}$ .

$\sqrt{\frac{y (49 x^{3} y)}{y}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\sqrt{\frac{y (49 x^{3} y)}{y^{1}}}$

Step 3.2.2

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

$\sqrt{\frac{y (49 x^{3} y)}{y \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$\sqrt{\frac{y (49 x^{3} y)}{y \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$\sqrt{\frac{49 x^{3} y}{1}}$

Step 3.2.5

Divide $49 x^{3} y$ by $1$ .

$\sqrt{49 x^{3} y}$

$\sqrt{49 x^{3} y}$

$\sqrt{49 x^{3} y}$

Step 4

Rewrite $49 x^{3} y$ as ${(7 x)}^{2} (x y)$ .

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Step 4.1

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} x^{3} y}$

Step 4.2

Factor out $x^{2}$ .

$\sqrt{7^{2} (x^{2} x) y}$

Step 4.3

Rewrite $7^{2} x^{2}$ as ${(7 x)}^{2}$ .

$\sqrt{{(7 x)}^{2} x y}$

Step 4.4

Add parentheses.

$\sqrt{{(7 x)}^{2} (x y)}$

$\sqrt{{(7 x)}^{2} (x y)}$

Step 5

Pull terms out from under the radical.

$7 x \sqrt{x y}$

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