Finding the Smallest Number to Add for a Perfect Square
The goal is to find the smallest number that, when added to 12519, results in a perfect square.
Step 1: Estimate the Square Root
First, find the approximate square root of the given number, 12519.
Calculate the square root: $\sqrt{12519} \approx 111.888$
Step 2: Identify the Next Integer
Since we need a perfect square *larger* than 12519, we look for the next whole number (integer) greater than the calculated square root.
The next integer after 111.888 is 112.
Step 3: Calculate the Next Perfect Square
Square the integer identified in the previous step to find the nearest larger perfect square.
Calculate $112^2$: $112 \times 112 = 12544$
So, 12544 is the smallest perfect square greater than 12519.
Step 4: Determine the Number to Add
Subtract the original number (12519) from the calculated perfect square (12544) to find the smallest number that needs to be added.
Number to add = $12544 - 12519$
Number to add = $25$
Therefore, adding 25 to 12519 gives 12544, which is a perfect square ($112^2$).
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Important Questions from Number System
Consider the following statements :
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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 ?
