Write the first 12 perfect squares and their square roots
The Correct Answer and Explanation is:
The first 12 perfect squares and their square roots are:
- 1 → Square root of 1 is 1
- 4 → Square root of 4 is 2
- 9 → Square root of 9 is 3
- 16 → Square root of 16 is 4
- 25 → Square root of 25 is 5
- 36 → Square root of 36 is 6
- 49 → Square root of 49 is 7
- 64 → Square root of 64 is 8
- 81 → Square root of 81 is 9
- 100 → Square root of 100 is 10
- 121 → Square root of 121 is 11
- 144 → Square root of 144 is 12
Explanation:
A perfect square is a number that is the product of an integer multiplied by itself. In other words, it’s a number that can be expressed as the square of an integer. For example, 4 is a perfect square because it can be written as ( 2 \times 2 ), where 2 is an integer. Similarly, 9 is a perfect square because it equals ( 3 \times 3 ), and 3 is an integer.
The square root of a perfect square is the number that, when multiplied by itself, gives the original perfect square. For example, the square root of 16 is 4, because ( 4 \times 4 = 16 ). The square root is essentially the inverse operation of squaring a number. Therefore, when you square a number, you get a perfect square, and when you find the square root of that perfect square, you get the number that was squared.
Mathematically, the square root is represented by the radical symbol ( \sqrt{} ). For instance, the square root of 25 is written as ( \sqrt{25} = 5 ), because ( 5 \times 5 = 25 ).
The square root function is important in many fields, including algebra, geometry, and even in real-world applications like architecture and engineering. Understanding the relationship between perfect squares and their square roots is fundamental to solving problems involving area, volume, and other mathematical calculations.