Precalculus Examples

$\sqrt{25 x} + \sqrt{x^{9}}$

Step 1

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} x} + \sqrt{x^{9}}$

Step 2

Pull terms out from under the radical.

$5 \sqrt{x} + \sqrt{x^{9}}$

Step 3

Rewrite $x^{9}$ as ${(x^{4})}^{2} x$ .

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Step 3.1

Factor out $x^{8}$ .

$5 \sqrt{x} + \sqrt{x^{8} x}$

Step 3.2

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$5 \sqrt{x} + \sqrt{{(x^{4})}^{2} x}$

$5 \sqrt{x} + \sqrt{{(x^{4})}^{2} x}$

Step 4

Pull terms out from under the radical.

$5 \sqrt{x} + x^{4} \sqrt{x}$

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