find a fraction whos square root is between 2 and 3 

To find a fraction whose square root lies between 2 and 3, we need to find a fraction \( \frac{a}{b} \) such that:

\[
2 < \sqrt{\frac{a}{b}} < 3
\]

Squaring all sides of the inequality:

\[
4 < \frac{a}{b} < 9
\]

Now we just need to find a fraction \( \frac{a}{b} \) that lies between 4 and 9. One possible solution is:

\[
\frac{a}{b} = \frac{20}{5} = 4.8
\]

Since \( \frac{20}{5} = 4.8 \), we can check its square root:

\[
\sqrt{\frac{20}{5}} = \sqrt{4.8} \approx 2.19
\]

This satisfies the condition that the square root is between 2 and 3.

Would you like further clarification or other examples?

Here are 5 related questions:

1. What is the square root of 7/2?
2. How do you find the square root of a decimal number?
3. Can you find another fraction whose square root is between 2 and 3?
4. How do you simplify the square root of a fraction?
5. How would you solve inequalities involving square roots?

**Tip:** When solving inequalities involving square roots, squaring both sides simplifies the problem but remember to check the validity of the solution afterward.

Find a fraction whose square root is between 2 and 3

Learn how to find a fraction whose square root lies between 2 and 3. This problem explores inequalities and square roots, providing a detailed step-by-step solution suitable for students in Grades 8-10.

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