Question

Write three-digit numbers ending with 0, 1, 4, 5, 6, 9 one for each digit, but none of them is a perfect square.

Answer 1

Hint: Start by selecting each digit one by one and randomly choose a three-digit number ending with the selected digit. Once you select a three-digit number, check whether it’s a perfect square or not.

Complete step-by-step answer:

First, let us find a three-digit number ending with 0. So, let’s take it to be 100. But 100 is a perfect square so we can’t take it. Moving forward, let us take number 110, and it’s not a perfect square as well.

We are next moving to the digit 1. The three-digit number ending with 1 can be 101, and it’s not a perfect square as well, making it a valid answer.

We are now moving to the digit 4. The three-digit number ending with 4 can be 104, and it’s not a perfect square as well, making it a valid answer.

Similarly, for digit 5, the number can be 105. Again, for digit 6, the number is 106, and for 9 the number is 109. Also, we can see that 105, 106, and 109 are not perfect squares so they can be selected.

Therefore, three-digit numbers ending with 0, 1, 4, 5, 6, 9, and none of them being a perfect square are 110, 101, 104, 105, 106, and 109, respectively.

Note: For your ease, you can select two consecutive numbers that have their squares lying between 100 to 999, i.e., their squares are three-digit numbers. Then you can say that all the numbers lying between their squares are not perfect squares.