What is the simplest radical form of sqrt(75/100)?

To determine the simplest radical form of ( \sqrt{\frac{75}{100}} ), we start by simplifying the expression under the square root.

First, divide both the numerator and denominator by 25, which is the greatest common divisor:

[

\frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}

]

Now we take the square root of this simplified fraction:

[

\sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}} = \frac{\sqrt{3}}{2}

]

This is the simplest radical form of the original expression. Therefore, the correct answer is ( \frac{\sqrt{3}}{2} ), which matches the choice labeled as C.

This approach effectively shows how to simplify radicals and apply properties of square roots, leading to a clear final answer.