find the smallest 6 digit number which is a perfect square
Find the smallest 6 digit number which is a perfect square
Answer:
To find the smallest 6-digit number which is a perfect square, we need to determine the smallest possible value of ( n ) such that ( n^2 ) results in a 6-digit number. A 6-digit number ranges from 100000 to 999999.
Solution By Steps:
-
Find the square root boundaries of 100000 and 999999:
- Calculate the square roots of these numbers to find the range of possible ( n ) values.
\sqrt{100000} \approx 316.23\sqrt{999999} \approx 999.99 -
Determine the smallest integer ( n ) greater than or equal to ( \sqrt{100000} ):
- Since ( n ) must be an integer, we round up ( \sqrt{100000} ).
n = \lceil 316.23 \rceil = 317 -
Verify ( 317^2 ):
- Calculate ( 317^2 ) to check if it is a 6-digit number.
317^2 = 100489- Since ( 100489 ) is indeed a 6-digit number, we confirm that ( 317 ) is the smallest integer such that its square is a 6-digit number.
Final Answer:
The smallest 6-digit number which is a perfect square is ( \boxed{100489} ).