banner

Squares & Perfect Squares – Explanation & Examples

In mathematics, a square is a product of a whole number with itself. For instance, the product of a number 2 by itself is 4. In this case, 4 is termed as a perfect square.

A square of a number is denoted as n × n. Similarly, the exponential notation of the square of a number is n 2, usually pronounced as “n” squared. Square numbers are usually non-negative.

What is a Perfect Square?

A perfect square is a number that is generated by multiplying two equal integers by each other. For example, the number 9 is a perfect square because it can be expressed as a product of two equal integers: 9 = 3 x 3.

The first 25 perfect squares can be generated as shown in the table below:

Example 1

IntegerPerfect square
1 x 11
2 x 24
3 x 39
4 x 416
5 x 525
6 x 636
7 x 749
8 x 864
9 x 981
10 x 10100
11 x 11121
12 x 12144
13 x 13169
14 x 14196
15 x 15225
16 x 16256
17 x 17289
18 x 18324
19 x 19361
20 x 20400
21 x 21441
22 x 22484
23 x 23529
24 x 24576
25 x 25625

 

How can you tell if a number is a Perfect Square?

There are many ways of determining if a number is perfect. A given number can be checked whether it is a perfect square using repeated division by prime factors.

Example 2

For example, to check whether 441 is a perfect square:

  • Start by factorizing a number.

441 = 3 × 3 × 7 × 7

  • Both numbers exist twice. Make two sets.
    441 = 3 × 7 × 3 × 7
  • Multiply them.

= 21 × 21

  • It can be written as

= 212

  • Hence, 441 is a perfect square.

You can also check whether a given number is a perfect square by finding the number’s square root. If the square root of a number is a whole number, then the number is a perfect square

For instance, the square root of 16 is 4. The square root of a number like 24 is not a whole number. Therefore, 24 is not a perfect square.

Practice Questions

1. The area of a square coffee table is $3600$ cm². Which of the following shows the length of one side of the coffee table?

2. What is the length of a square flower garden if the area is 81 square yards.

3. The length of a square piece of paper is 4 cm. What is the area of the paper?

4. A square room has an area of 64 square feet. What is the length of a carpet needed to cover the floor of this room perfectly?

5. A square football pitch has a perimeter of $400$ meters. What is the area of this pitch?

6. The perimeter wall of a square compound is $480$ meters. What is the length and area of the compound?

7. The area of a square plot of land is $10000$ m². What is the perimeter of the plot of land?

8. A farmer divided his ranch into $5$ equal square sections. Suppose the length of each section is $50$ meters. What is the total area of the ranch?


 

Previous Lesson | Main Page | Next Lesson

5/5 - (26 votes)