Calculus Examples

$\sqrt{9 a b^{3}}$

Step 1

Rewrite $9 a b^{3}$ as ${(3 b)}^{2} (a b)$ .

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Step 1.1

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

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

Step 1.2

Factor out $b^{2}$ .

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

Step 1.3

Move $a$ .

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

Step 1.4

Rewrite $3^{2} b^{2}$ as ${(3 b)}^{2}$ .

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

Step 1.5

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

$3 b \sqrt{a b}$

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