Trigonometry Examples

$\frac{\sqrt{6 a^{3} b^{2}}}{\sqrt{3 a b}}$

Step 1

Combine $\sqrt{6 a^{3} b^{2}}$ and $\sqrt{3 a b}$ into a single radical.

$\sqrt{\frac{6 a^{3} b^{2}}{3 a b}}$

Step 2

Reduce the expression $\frac{6 a^{3} b^{2}}{3 a b}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $6 a^{3} b^{2}$ .

$\sqrt{\frac{3 (2 a^{3} b^{2})}{3 a b}}$

Step 2.2

Factor $3$ out of $3 a b$ .

$\sqrt{\frac{3 (2 a^{3} b^{2})}{3 (a b)}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{3 (2 a^{3} b^{2})}{3 (a b)}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{2 a^{3} b^{2}}{a b}}$

$\sqrt{\frac{2 a^{3} b^{2}}{a b}}$

Step 3

Cancel the common factor of $a^{3}$ and $a$ .

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Step 3.1

Factor $a$ out of $2 a^{3} b^{2}$ .

$\sqrt{\frac{a (2 a^{2} b^{2})}{a b}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $a b$ .

$\sqrt{\frac{a (2 a^{2} b^{2})}{a (b)}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{a (2 a^{2} b^{2})}{a b}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{2 a^{2} b^{2}}{b}}$

$\sqrt{\frac{2 a^{2} b^{2}}{b}}$

$\sqrt{\frac{2 a^{2} b^{2}}{b}}$

Step 4

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

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Step 4.1

Factor $b$ out of $2 a^{2} b^{2}$ .

$\sqrt{\frac{b (2 a^{2} b)}{b}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

$\sqrt{\frac{b (2 a^{2} b)}{b^{1}}}$

Step 4.2.2

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

$\sqrt{\frac{b (2 a^{2} b)}{b \cdot 1}}$

Step 4.2.3

Cancel the common factor.

$\sqrt{\frac{b (2 a^{2} b)}{b \cdot 1}}$

Step 4.2.4

Rewrite the expression.

$\sqrt{\frac{2 a^{2} b}{1}}$

Step 4.2.5

Divide $2 a^{2} b$ by $1$ .

$\sqrt{2 a^{2} b}$

$\sqrt{2 a^{2} b}$

$\sqrt{2 a^{2} b}$

Step 5

Rewrite $2 a^{2} b$ as $a^{2} \cdot (2 b)$ .

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Step 5.1

Reorder $2$ and $a^{2}$ .

$\sqrt{a^{2} \cdot 2 b}$

Step 5.2

Add parentheses.

$\sqrt{a^{2} \cdot (2 b)}$

$\sqrt{a^{2} \cdot (2 b)}$

Step 6

Pull terms out from under the radical.

$a \sqrt{2 b}$

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