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.
Similar Questions
- The value of $1+2+3+...+30+31+30+29+...+3+2+1 =$ ?
- Find the sum of the face values of 6 and 5 in 61827354.
- Which of the following statements is false?
- How many factors of $2^3 \times 3^3 \times 5^4 \times 7^2$ are divisible by 50 but not by 100?
- What is the number of divisors of 120?
- What is the place value of 3 in 367892141?
- The sum of 4 consecutive odd numbers is 160. Find the smallest number.
- A number consists of 3 digits whose sum is 18 and the middle digit is equal to the sum of the other two. If the number increases by 297 when its digits are reversed, then what is the number?
- Find sum of the smallest and the largest positive numbers of 6 digits which contains only digits 0, 4, 6 and each of these digits appears at least once:
- Find the value of D if $1216 - 32D = DDD$ is divisible by 8.
Important Questions from Number System
What is the value of 1 2 + 2 2 + 3 2 + ......21 2 ?
Which sequence is correct to represent the hierarchical chain of number system?
(Where N - Natural Numbers
W - Whole Numbers
Q - Rational Numbers
Z - Integers)
What must be added to 45680 to make it exactly divisible by 9?
How many zeroes are there at the end of the following product?
1 x 5 x 10 x 15 x 20 x 25 x 30 x 35 x 40 x 45 x 50 x 55 x 60
Let XYZ be a three-digit number, where (x + y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by
