Algebra Examples

3 \sqrt{125}

$3 \sqrt{125}$

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

$125$ .

3 \sqrt{25 (5)}

$3 \sqrt{25 (5)}$

Step 1.2

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

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

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

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

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

Step 2

Pull terms out from under the radical.

3 (5 \sqrt{5})

$3 (5 \sqrt{5})$

Step 3

Multiply

5

$5$ by

3

$3$ .

15 \sqrt{5}

$15 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

15 \sqrt{5}

$15 \sqrt{5}$

Decimal Form:

33.54101966 \dots

$33.54101966 \dots$

3 \sqrt[]{125}

$3 \sqrt[]{125}$

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

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