Evaluate square root of 125/80

$\sqrt{\frac{125}{80}}$

Step 1

Cancel the common factor of $125$ and $80$ .

Factor $5$ out of $125$ .

$\sqrt{\frac{5 (25)}{80}}$

Cancel the common factors.

Factor $5$ out of $80$ .

$\sqrt{\frac{5 \cdot 25}{5 \cdot 16}}$

Cancel the common factor.

$\sqrt{\frac{5 \cdot 25}{5 \cdot 16}}$

Rewrite the expression.

$\sqrt{\frac{25}{16}}$

Step 2

Rewrite $\sqrt{\frac{25}{16}}$ as $\frac{\sqrt{25}}{\sqrt{16}}$ .

$\frac{\sqrt{25}}{\sqrt{16}}$

Step 3

Simplify the numerator.

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

$\frac{\sqrt{5^{2}}}{\sqrt{16}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{5}{\sqrt{16}}$

Step 4

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$\frac{5}{\sqrt{4^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{5}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{4}$

Decimal Form:

$1.25$

Mixed Number Form:

$1 \frac{1}{4}$