Question

Find the least numbers which must be added to each of the following numbers to get a perfect square 525

Answer 1

Hint: A product of a number with the same number itself is called a square of that number. A perfect square number is a number obtained by the product of a whole number with itself. That is, A perfect square is a square of a whole number.

Complete step-by-step solution:
It is given that we need to find a number that can be added to 525 so that we get a perfect square number.
We will start increasing the given number by one at a time and check whether that is a perfect square number.
Let us increase the given by one, \[525 \to 525 + 1 = 526\]
Now let us check whether \[526\] is a perfect square or not. Let’s take a square root.
\[\sqrt {526} \simeq 22.94\]
We got a decimal number. Thus, it is not a perfect square.
Let us increase the given by two, \[525 + 2 = 527\]
Now let us check whether \[527\] is a perfect square or not. Let’s take a square root.
\[\sqrt {527} \simeq 22.96\]
We got a decimal number. Thus, it is not a perfect square.
Let us increase the given by three, \[525 + 3 = 528\]
Now let us check whether \[528\] is a perfect square or not. Let’s take a square root.
\[\sqrt {528} \simeq 22.98\]
We got a decimal number. Thus, it is not a perfect square.
Let us increase the given by four, \[525 + 4 = 529\]
Now let us check whether \[529\] is a perfect square or not. Let’s take a square root.
\[\sqrt {529} = 23\]
Now, we have a perfect square. Thus, the least number is \[4\] which by adding to \[525\] we get a perfect square.

Note: Since they have asked for the least number, we started to add one by one starting from one, two, and so on. After increasing the number, we will check whether it is a perfect square or not by taking the square root of that number.