Finding the Least Number to Add for a Perfect Square
The goal is to find the smallest non-negative integer that, when added to 6412, results in a perfect square.
Step 1: Estimate the Square Root
First, find the square root of the given number, 6412.
$ \sqrt{6412} \approx 80.07 $
Step 2: Identify the Next Integer
Since the square root is approximately 80.07, the next whole number is 81. The perfect square immediately greater than 6412 will be the square of 81.
Step 3: Calculate the Next Perfect Square
Calculate the square of 81:
$ 81^2 = 81 \times 81 = 6561 $
This number, 6561, is the smallest perfect square greater than 6412.
Step 4: Determine the Number to Add
To find the least number that must be added to 6412 to get 6561, subtract 6412 from 6561.
Number to add = $ 6561 - 6412 $
Number to add = $ 149 $
Conclusion
Therefore, the least number which must be added to 6412 to get a perfect square is 149.
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2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
If the sum S is divided by 8, what is the remainder ?
If the sum S is divided by 60, what is the remainder ?
Find the sum of squares of the greatest value and the smallest value of K in the number so that the number 45082K is divisible by 3.
How many composite numbers are there from 53 to 97 ?
