Finding the Smallest Number for a Perfect Square
The objective is to determine the smallest integer that needs to be added to 2378 to obtain a perfect square.
Identifying the Nearest Larger Perfect Square
First, calculate the square root of the number 2378.
$ \sqrt{2378} \approx 48.76 $
To find the next perfect square, we consider the integer immediately following 48.76, which is 49.
Now, calculate the square of 49:
$ 49^2 = 2401 $
Thus, 2401 is the smallest perfect square that is greater than 2378.
Calculating the Required Addition
The smallest number that must be added is the difference between this larger perfect square (2401) and the original number (2378).
Number to add $= 2401 - 2378 $
Number to add $= 23 $
Result
Adding 23 to 2378 results in 2401, which is a perfect square ($49^2$). Therefore, the smallest number required is 23.
Similar Questions
- Which of these is both an Integer and a Whole number?
- Which of the following is a non-zero number that belongs to every set: Whole, Integer, Rational, and Real?
- Which of the following is a perfect square and an Integer?
- The set of real numbers includes which of the following?
In the following examples, a number is coded as three digits — representing the remainders when the number is divided by 3, 7, and 11, respectively.
Example 1: $53 \rightarrow 53 \div 3 = 17 \text{ R} 2$, $53 \div 7 = 7 \text{ R } 4$, $53 \div 11 = 4 \text{ R } 9 \rightarrow \text{ Code: } 2, 4, 9$
Example 2: $68 \rightarrow 68 \div 3 = 22 \text{ R} 2$, $68 \div 7 = 9 \text{ R } 5$, $68 \div 11 = 6 \text{ R } 2 \rightarrow \text{ Code: } 2, 5, 2$
By following this method, which is the least number which would have the code - 2, 2, 2?- Which roll number has only prime digits?
- A student was asked to find the sum of first 20 odd numbers. His answer was 400. Correct?
- Which roll number is a perfect cube?
- Which roll number has a digital root equal to 9? Digital root = sum of digits until one digit remains.
Which of the following statement is TRUE for Whole Numbers?
Important Questions from Number System
Consider the following statements :
1. (25)! + 1 is divisible by 26
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 ?
