When is an integer a perfect square

The first column shows the natural number and the second column shows the square of the natural number. You can easily find the square of a natural number by multiplying it by itself. Look at these lists of perfect squares to have a better understanding of perfect square numbers 1 to Observe the last digit of the perfect square numbers 1 to 20 as given in the table above. You will notice that they end with any one of these digits 0, 1, 4, 5, 6, or 9.

After trying various perfect square numbers you would have observed an important property of perfect squares. Numbers that have any of the digits 2, 3, 7, or 8 in their units place are non-perfect square numbers, whereas, numbers that have any of the digits 0, 1, 4, 5, 6, or 9 in their units place might be perfect squares. The following observations can be made to identify a perfect square. Let us look at a few deviations from the above-defined rules of a perfect square number.

The numbers and both end with the digit 9 but is a perfect square, whereas is not. If the number ends with the digit 0, then you may look for the following: How many zeros are there at the end of the number?

Let's say we have a number If there are an odd number of zeros, then it's definitely not a perfect square. Thus, it's not a perfect square. If there are an even number of zeros, then it might be a perfect square. Another way to check whether a number is a perfect square or not is by calculating the square root of the given number. If the square root is a whole number, then it is a perfect square. If the square root is not a whole number, then the given number is not a perfect square. For example, to check whether 24 is a perfect square or not, let us calculate its square root.

Let us take another example of the number We can see that 9 is a whole number, therefore, 81 is a perfect square. These can be applied to square a number in a very short time.

In other words, this can be used to calculate the square of a large number without using the long multiplication method. Numbers Ending with Digit 5: Let's consider a number ending with 5, like, Now, we can find the square of 65 through a sequence of four simple steps. First, we need to separate the numbers 6 and 5.

Next, multiply 6 with its successor, i. Now for the third step, square the number 5 to get Further, for the final step write the digits of the second step, followed by The final answer for the square of 65 is Example 1: In an auditorium, the number of rows is the same as the number of columns. If there are 60 chairs in a row, how many chairs are there in the auditorium?

It is given that the number of rows is the same as the number of columns. Active Oldest Votes. Add a comment. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Linked 0. Related 3. Next Check if a number is perfect square without finding square root.

Recommended Articles. Count of pair of integers x , y such that difference between square of x and y is a perfect square. Check if a number can be represented as a sum of a Prime Number and a Perfect Square. Print all Perfect Numbers from an array whose sum of digits is also a Perfect Number. Probability of getting a perfect square when a random number is chosen in a given range. Article Contributed By :. Aditya Darekar. Easy Normal Medium Hard Expert.

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