Perfect Square Calculator
A perfect square calculator is a free online tool that tells you whether a number is a perfect square or not
What is a Perfect Square Calculator?
A perfect square calculator is a free online tool that tells you whether a number is a perfect square or not. This calculator helps you to calculate faster and gives you the result within a few seconds.
Perfect Square Calculator
NOTE: Enter numbers upto 5 digits and enter whole numbers only.
How to Use the Perfect Square Calculator?
Follow the steps given below to use the calculator:
- Step 1: Enter a number in the input box.
- Step 2: Click on "Check" to know whether the number is a perfect square or not.
- Step 3: Click on "Reset" to clear the field and enter the new number.
What is a Perfect Square?
A perfect square is a number that can be expressed as the product of exactly two equal integers. For example, 62 = (6 × 6) = 36. Here, 36 is a perfect square because it is the product of two equal integers, 6 × 6 = 36. However, 21 is not a perfect square because it cannot be expressed as the product of two equal integers. (7 × 3 = 21). This concept can be understood in another way.
If a number 'a' is multiplied with 'a', it gives 'n'. This can be written as a × a = n, or, a2 = n.
Here, "a" is called the square root of n, and this is represented as: a = √n. Now, after calculating the square root of n, if we get to know that "a" is a whole number, and not a decimal number, then we can say that "n" is a perfect square. For example, if n = 89, then a = √89 = 9.43, which is in the decimal form and not a whole number. This means 89 is not a perfect square. In simple words, once we find the square root of the given number, we can get to know if it is a perfect square or not. Let us take another example. If n = 64, then a = √64= 8, which is a whole number. This shows that 64 is a perfect square.
Solved Examples on Perfect Square Calculator
Example 1:
Find out if 81 is a perfect square or not.
Solution:
We will calculate the square root of 81 to find out if it is a perfect square or not. If the answer is a whole number, then it is a perfect square.
\(a = \sqrt{n}\\ \,\,\,= \sqrt{81} \\ \,\,\,= \sqrt{9 \times 9}\\ \,\,\,= 9 \)
As we can see that 9 is a whole number. Therefore, 81 is the perfect square.
Example 2:
Find out if 144 is a perfect square or not.
Solution:
We will calculate the square root of 144 to find out if it is a perfect square or not. If the answer is a whole number, then it is a perfect square.
\(a = \sqrt{n}\\ \,\,\,= \sqrt{144} \\ \,\,\,= \sqrt{12 \times 12}\\ \,\,\,= 12\)
As we can see that 12 is a whole number. Therefore, 144 is the perfect square.
Example 3:
Find out if 220 is a perfect square or not.
Solution:
We will calculate the square root of 220 to find out if it is a perfect square or not. If the answer is a whole number, then it is a perfect square.
\(a = \sqrt{n}\\ \,\,\,= \sqrt{220} \\ \,\,\,= 2\sqrt{55}\)
As we can see that answer is not a whole number. Therefore, 220 is not perfect square.
Now, try the calculator to find out whether the following numbers are perfect squares or not.
- 729
- 343