Algebra Examples

\sqrt{125}

$\sqrt{125}$

Step 1

Rewrite

125

$125$ as

5^{2} \cdot 5

$5^{2} \cdot 5$ .

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Step 1.1

Factor

25

$25$ out of

125

$125$ .

\sqrt{25 (5)}

$\sqrt{25 (5)}$

Step 1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

5 \sqrt{5}

$5 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

5 \sqrt{5}

$5 \sqrt{5}$

Decimal Form:

11.18033988 \dots

$11.18033988 \dots$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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