The square root of which of the following is a rational number?

we can solve this by option by option 

Square root of rational numbers in the form of fractions

Step I: Obtain the fraction
Step II: If the given square root of the numerator and the denominator are the square roots of numerator and denominator respectively of the given fraction.
Step III: Find the square root of the numerator and denominator separately.
Step IV: Obtain the fraction whose numerator and denominator are the square roots of numerator and denominator respectively of the given fraction.
Step V: The fraction obtained in Step IV is the square root of the given fraction.

so by going option ,

we can covert 1489.96 into fracation = $$1489\ \frac{24}{25}$$

also write as $$\frac{37249}{25}$$

here 37249 is the square root of 193 and 25 is of 5 

So option a is correct ans