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Simplify ( square root of 125)÷5

$\sqrt{125} \div 5$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt{125}}{5}$

Step 2

Simplify the numerator.

Rewrite

$125$ as

$5^{2} \cdot 5$ .

Factor

$25$ out of

$125$ .

$\frac{\sqrt{25 (5)}}{5}$

Rewrite

$25$ as

$5^{2}$ .

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

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

Pull terms out from under the radical.

$\frac{5 \sqrt{5}}{5}$

$\frac{5 \sqrt{5}}{5}$

Step 3

Cancel the common factor of

$5$ .

Cancel the common factor.

$\frac{5 \sqrt{5}}{5}$

Divide

$\sqrt{5}$ by

$1$ .

$\sqrt{5}$

$\sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{5}$

Decimal Form:

$2.23606797 \dots$

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