Question

Find the least number to be added to $12675$ to get a perfect square.

Answer 1

Hint: Here we have to find the square of nearest numbers and compare the squares with the given number if it is less than the given number then find the square of next number, because we have to add some number to the given number in order to make it as a perfect square of any number.

Complete step by step solution:
Now consider the given number 12675
Let us consider the first 3 numbers 126. We know that 121 is a perfect square of the number 11.
So, we consider the number 110 when we square this number, we get
\[110 \times 110 = 12100\]
Now replace the unit place value 0 by 1 and square it, we get
\[111 \times 111 = 12321\]
Now replace the unit place value 1 by 2 and square it, we get
\[112 \times 112 = 12544\]
Now replace the unit place value 2 by 3 and square it, we get
\[113 \times 113 = 12769\]
Therefore, the number 12675 lies between the squares of 112 and 113
Now we will subtract the given number from 12769 and hence we get
\[12769 - 12675 = 94\]
Therefore, we have to 94 to 12675 to make it a perfect square.
Suppose when we add 94 to 12675, we get
\[12675 + 94 = 12769\]

Where 12769 is a perfect square of the number 113.

Note: To determine the perfect square we must know the squares of the number which makes us to find the value in an easy way. We must also know about the table of multiplication if we go wrong in the multiplication the whole answer will go wrong. We start this method by guessing or trial method.