Algebra Examples

$\sqrt{75}$

Step 1

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.1

Factor $25$ out of $75$ .

$\sqrt{25 (3)}$

Step 1.2

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

$\sqrt{5^{2} \cdot 3}$

Step 2

Pull terms out from under the radical.

$| 5 | \sqrt{3}$

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$5 \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{3}$

Decimal Form:

$8.66025403 \dots$