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# 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, 6^{2} =^{ }(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, a^{2 }= 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

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