The square of a number consists of digits 0, 2, 3, 5. find the number.

The required number is 55.

SOLUTION:

Given that, the Square of a number consists of digits 0, 2, 3, 5.  We have to find the number.

Now, 0 can’t be in ten thousands place, as if it is there, the square number will be 3 digits and we know that no 3 digit square has 2, 3, 5 together in them.

We know that first 4 digit square is 1024 that is square of 32 and until 44 square i.e. 1936 we have 1 in ten thousands place, but we don’t have 1 in our list.

So we have to consider numbers from 45.

Now, 0 can’t be in ones place also as if we have to keep 0 in once place, then it should a square of number whose units digit is 0, thereby if square a number with units place 0, the result will be having 2 zeros in units place and tens place.

Generally, our required number will be two digit number as its square is having 4 digits.

So, possibilities of units place of our number are 0 – 9, as we excluded 0, remaining possibilities are 1 – 9.

Now, we know that, unit digit of a square term will be based on the unit digit of the number.

So, let us see pairs of unit digits in number and its result in square terms.  

1 – 1, 2 – 4, 3 – 9, 4 – 4, 5 – 5, 6 – 6, 7 – 9, 8 – 4, 9 – 1. As we can see only 5 results in 5 but remaining all results in numbers that are not in our list.

So, units digit is 5, so we have to check 45, 55, 65, 95

Now, their squares are 2025, 3025, 4225, ….

Here, we got 3025 as square of 55, it has 0, 2, 3, 5 .