Final answer:
To find a rational number between √3 and √6, we can rationalize the denominators and simplify the expressions. The rational number (√3 + √6) / 2√3 lies between √3 and √6.
Step-by-step explanation:
To find a rational number between √3 and √6, we can rationalize the denominators and simplify the expressions.
We know that √3 can be written as (√3 * √3) / √3 = 3 / √3. Similarly, √6 can be written as (√6 * √6) / √6 = 6 / √6.
Now, we need to find a common denominator and make the denominators equal. The LCM of √3 and √6 is √18.
Thus, a rational number between √3 and √6 is (3/√3 + 6/√6) / 2 = (√3 + √6) / 2√3.
Learn more about Finding a rational number between two square roots