Question

The number of digits in a perfect square is even. If true then enter 1, if false then enter 0.

Answer 1

Hint: When solving these types of questions where it is asked how a number behaves, select the simplest numbers possible and work with them. Then, just to confirm it, move to another number which happens to be a 2-digit number if you started with a 1-digit number, 3-digit one if the first number taken was of 2-digits and so on.

Complete Step by Step Solution:
The square of a number is the value obtained when a number is multiplied by itself.
When we talk about squares, every number is a square of some other number. For example, if we consider 2, it is the square of 1.4142, 3 is the square of 1.7320, 5 is the square of 2.2360, 6 is the square of 2.4494, 7is the square of 2.6457 and 8 is the square of 2.8284.
Now you might be wondering that from 1-9, we included all numbers but left out 1, 4 and 9. They too are squares of some numbers but they are a different type of square called perfect squares. This means that the numbers used to get these squares are whole numbers. Observe that 1 is the square of itself, 4 is the square of 2, 9 is the square of 3.
Now looking back at the question, we were asked if a perfect square has only an even number of digits and here, we saw that the squares of 1, 2 and 3 have an odd number of digits. So, the statement is false. After that, the squares of 4-9, all have an even number of digits. Thus, we look at the square of 10 too which is 100, also a perfect square which is made of 3 digits.
Thus, the statement above is false because we proved that the squares of 1, 2, 3 and 10, all have odd numbers of digits and also there are many such perfect squares with odd numbers of digits. As such we ought to enter 0.

Note:
A square can either be a whole number or a decimal number depending on the number using which the square is obtained but it will never be a negative number as the property of squaring compels us to multiply the number with itself including the sign attached to it and minus sign multiplied with minus sign becomes plus sign.