Finite Math Examples

$\sqrt{x^{3} - x^{2}} + \sqrt{81 x - 81}$

Step 1

Factor $x^{2}$ out of $x^{3} - x^{2}$ .

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Step 1.1

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

$\sqrt{x^{2} x - x^{2}} + \sqrt{81 x - 81}$

Step 1.2

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

$\sqrt{x^{2} x + x^{2} \cdot - 1} + \sqrt{81 x - 81}$

Step 1.3

Factor $x^{2}$ out of $x^{2} x + x^{2} \cdot - 1$ .

$\sqrt{x^{2} (x - 1)} + \sqrt{81 x - 81}$

Step 2

Pull terms out from under the radical.

$x \sqrt{x - 1} + \sqrt{81 x - 81}$

Step 3

Factor $81$ out of $81 x - 81$ .

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Step 3.1

Factor $81$ out of $81 x$ .

$x \sqrt{x - 1} + \sqrt{81 (x) - 81}$

Step 3.2

Factor $81$ out of $- 81$ .

$x \sqrt{x - 1} + \sqrt{81 (x) + 81 (- 1)}$

Step 3.3

Factor $81$ out of $81 (x) + 81 (- 1)$ .

$x \sqrt{x - 1} + \sqrt{81 (x - 1)}$

Step 4

Rewrite $81 (x - 1)$ as ${(3^{2})}^{2} (x - 1)$ .

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Step 4.1

Rewrite $81$ as $9^{2}$ .

$x \sqrt{x - 1} + \sqrt{9^{2} (x - 1)}$

Step 4.2

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

$x \sqrt{x - 1} + \sqrt{{(3^{2})}^{2} (x - 1)}$

Step 5

Pull terms out from under the radical.

$x \sqrt{x - 1} + 3^{2} \sqrt{x - 1}$

Step 6

Raise $3$ to the power of $2$ .

$x \sqrt{x - 1} + 9 \sqrt{x - 1}$