A perfect square number lies between 1700 and 1800 and is divisible by 9. Find that number and its square root.

Correct option is C

Given:
The number is a perfect square.
It lies between 1700 and 1800.
It is divisible by 9.
Formula Used:
A number is divisible by 9 if the sum of its digits is divisible by 9.
Solution:
Find the squares of numbers that fall near the 1700 to 1800 range.
$$40^2$$​ = 1600
$$41^2$$​= 1681
$$42^2$$​ = 1764
$$43^2$$​ = 1849
The only perfect square strictly between 1700 and 1800 is 1764.
Check divisibility by 9 for 1764.
Sum of digits = 1 + 7 + 6 + 4 = 18
Since 18 is divisible by 9, 1764 is divisible by 9.
The number is 1764 and its square root is 42.
Final Answer
So the correct answer is (c)