To simplify \( \sqrt{\frac{6}{75}} \):

1. Simplify the fraction \( \frac{6}{75} \). The greatest common divisor (GCD) of 6 and 75 is 3.
   \[
   \frac{6}{75} = \frac{6 \div 3}{75 \div 3} = \frac{2}{25}
   \]

2. Now simplify \( \sqrt{\frac{2}{25}} \) by taking the square root of both the numerator and the denominator:
   \[
   \sqrt{\frac{2}{25}} = \frac{\sqrt{2}}{\sqrt{25}} = \frac{\sqrt{2}}{5}
   \]

Thus, \( \sqrt{\frac{6}{75}} = \frac{\sqrt{2}}{5} \).

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. Simplify \( \sqrt{\frac{8}{100}} \).
2. What is the square root of \( \frac{9}{16} \)?
3. Simplify \( \sqrt{50} \).
4. Calculate \( \sqrt{\frac{12}{144}} \).
5. What is the decimal approximation of \( \frac{\sqrt{2}}{5} \)?

**Tip:** When simplifying square roots of fractions, simplify the fraction first to make the process easier.

Learn how to simplify the square root of 6/75 with a detailed solution. First, simplify the fraction 6/75 to 2/25, then apply square root rules to get the final answer, √2/5. This problem covers key math concepts such as simplifying fractions and square roots, suitable for students in Grades 6-8.

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