Square & Square Root (â) : āĻŦā§°ā§āĻ āĻā§°ā§ āĻŦā§°ā§āĻāĻŽā§āĻ˛ā§° āĻ¸āĻšāĻ āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž
The square of a number means multiplying the number by itself. (āĻā§āĻ¨ā§ āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻŦā§°ā§āĻ āĻŽāĻžāĻ¨ā§ āĻ¸ā§āĻ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§āĻ āĻ¨āĻŋāĻā§āĻā§°ā§ āĻā§āĻŖ āĻā§°āĻžāĨ¤)
Formula / āĻ¸ā§āĻ¤ā§ā§° : √a2 = a
Examples / āĻāĻĻāĻžāĻšā§°āĻŖ
1. √25 = 5, Because : 5 × 5 = 25 : āĻāĻžā§°āĻŖ : ā§Ģ × ā§Ģ = ā§¨ā§Ģ
2. √49 = 9 , Because : 9 × 9 = 49 : āĻāĻžā§°āĻŖ : ā§¯ × ā§¯ = ā§Žā§§
Easy Trick / āĻ¸āĻšāĻ āĻā§āĻļāĻ˛
- Square → Multiply the number by itself (āĻŦā§°ā§āĻ → āĻ¸āĻāĻā§āĻ¯āĻžāĻā§āĻ āĻ¨āĻŋāĻā§āĻā§°ā§ āĻā§āĻŖ āĻā§°āĻ)
- Square Root → Find the original number (āĻŦā§°ā§āĻāĻŽā§āĻ˛ → āĻŽā§āĻ˛ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ āĻŦāĻŋāĻāĻžā§°āĻ)
2) Why is it called a Square ? (āĻāĻ¯āĻŧāĻžāĻ Square āĻāĻŋāĻ¯āĻŧ āĻā§ā§ąāĻž āĻšāĻ¯āĻŧ ?)
It is called a square because equal sides form the area of a square shape. (āĻāĻ¯āĻŧāĻžāĻ Square āĻā§ā§ąāĻž āĻšāĻ¯āĻŧ āĻāĻžā§°āĻŖ āĻ¸āĻŽāĻžāĻ¨ āĻŦāĻžāĻšā§āĻ¯ā§āĻā§āĻ¤ āĻāĻāĻžā§°ā§° āĻā§āĻˇā§āĻ¤ā§ā§°āĻĢāĻ˛ side × side āĻā§°āĻŋ āĻĒā§ā§ąāĻž āĻ¯āĻžāĻ¯āĻŧāĨ¤)
Example: If one side of a square is 4 cm:
Area = 4 × 4 = 16 cm2
So, 16 is the square of 4. (āĻ¸ā§āĻ¯āĻŧā§, ā§§ā§Ŧ āĻšā§āĻā§ ā§Ē ā§° āĻŦā§°ā§āĻāĨ¤)
3) Squares of Numbers from 1 to 10 (ā§§ ā§° āĻĒā§°āĻž ā§§ā§Ļ āĻ˛ā§ āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻŦā§°ā§āĻ)
1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100
These are called perfect squares. (āĻāĻ¯āĻŧāĻžāĻ Perfect Squares āĻā§ā§ąāĻž āĻšāĻ¯āĻŧāĨ¤)
4) What is a Square Root ? āĻŦā§°ā§āĻāĻŽā§āĻ˛ (Square Root) āĻāĻŋ ?
A square root is the opposite of a square. āĻŦā§°ā§āĻāĻŽā§āĻ˛ āĻšā§āĻā§ āĻŦā§°ā§āĻā§° āĻŦāĻŋāĻĒā§°ā§āĻ¤āĨ¤
It tells us: “Which number was multiplied by itself ?” (“āĻā§āĻ¨ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§āĻ āĻ¨āĻŋāĻā§āĻā§°ā§ āĻā§āĻŖ āĻā§°āĻž āĻšā§āĻāĻŋāĻ˛ ?”)
Examples / āĻāĻĻāĻžāĻšā§°āĻŖ
- √25 = 5 Because: 5 × 5 = 25
- √36 = 6 Because: 6 × 6 = 36
5) Understanding with an Example (āĻāĻĻāĻžāĻšā§°āĻŖā§ā§°ā§ āĻŦā§āĻāĻž)
Square / āĻŦā§°ā§āĻ : 82 = 8 × 8 = 64
Square Root / āĻŦā§°ā§āĻāĻŽā§āĻ˛ : √64 = 8
So, square and square root are opposites of each other. (āĻ¸ā§āĻ¯āĻŧā§, āĻŦā§°ā§āĻ āĻā§°ā§ āĻŦā§°ā§āĻāĻŽā§āĻ˛ āĻĒā§°āĻ¸ā§āĻĒā§°ā§° āĻŦāĻŋāĻĒā§°ā§āĻ¤āĨ¤)
6) Perfect Squares (āĻĒā§ā§°ā§āĻŖ āĻŦā§°ā§āĻ āĻ¸āĻāĻā§āĻ¯āĻž) : Numbers formed by multiplying a whole number by itself are called perfect squares. (āĻāĻāĻž āĻĒā§ā§°ā§āĻŖ āĻ¸āĻāĻā§āĻ¯āĻžāĻ āĻ¨āĻŋāĻā§āĻā§°ā§ āĻā§āĻŖ āĻā§°āĻŋ āĻĒā§ā§ąāĻž āĻ¸āĻāĻā§āĻ¯āĻžāĻŦā§ā§°āĻ Perfect Square āĻā§ā§ąāĻž āĻšāĻ¯āĻŧāĨ¤)
Examples / āĻāĻĻāĻžāĻšā§°āĻŖ: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
7) Real Life uses of Squares & Square Roots (āĻŦāĻžāĻ¸ā§āĻ¤ā§ą āĻā§ā§ąāĻ¨āĻ¤ āĻŦā§āĻ¯ā§ąāĻšāĻžā§°)
- Finding area of squares (āĻŦā§°ā§āĻā§° āĻā§āĻˇā§āĻ¤ā§ā§°āĻĢāĻ˛ āĻāĻ˛āĻŋāĻā§ąāĻž)
- Construction and measurement (āĻ¨āĻŋā§°ā§āĻŽāĻžāĻŖ āĻā§°ā§ āĻā§āĻ-āĻŽāĻžāĻĒ)
- Mathematics and algebra (āĻāĻŖāĻŋāĻ¤ āĻā§°ā§ āĻŦā§āĻāĻāĻŖāĻŋāĻ¤)
- Games and puzzles (āĻā§āĻ˛ āĻā§°ā§ āĻ§āĻžāĻāĻ§āĻž)
- Engineering and science (āĻ āĻāĻŋāĻ¯āĻžāĻ¨ā§āĻ¤ā§ā§°āĻŋāĻ āĻā§°ā§ āĻŦāĻŋāĻā§āĻāĻžāĻ¨)
8) Revision : āĻĒā§āĻ¨ā§°āĻžāĻ˛ā§āĻāĻ¨āĻž
- Square = Number × itself (āĻŦā§°ā§āĻ = āĻ¸āĻāĻā§āĻ¯āĻž × āĻ¨āĻŋāĻā§āĻ)
- Square Root = Original number (āĻŦā§°ā§āĻāĻŽā§āĻ˛ = āĻŽā§āĻ˛ āĻ¸āĻāĻā§āĻ¯āĻž)
- Symbol of square = ² (āĻŦā§°ā§āĻā§° āĻāĻŋāĻšā§āĻ¨ = ²)
- Symbol of square root = √ (āĻŦā§°ā§āĻāĻŽā§āĻ˛ā§° āĻāĻŋāĻšā§āĻ¨ = √)
9) Practice
- What is the square of 7 ? (ā§ ā§° āĻŦā§°ā§āĻ āĻāĻŋāĻŽāĻžāĻ¨ ?)
- Find √81 (√81 āĻāĻ˛āĻŋāĻā§ąāĻžāĨ¤)
- What is 9² ? (9² āĻāĻŋāĻŽāĻžāĻ¨ ?)
- Find √100 (√100 āĻāĻ˛āĻŋāĻā§ąāĻžāĨ¤)
- Is 49 a perfect square ? (49 āĻāĻāĻž Perfect Square āĻ¨ā§āĻāĻŋ ?)
Easy Trick / āĻ¸āĻšāĻ āĻā§āĻļāĻ˛
- Square → Multiply the number by itself (āĻŦā§°ā§āĻ → āĻ¸āĻāĻā§āĻ¯āĻžāĻā§āĻ āĻ¨āĻŋāĻā§āĻā§°ā§ āĻā§āĻŖ āĻā§°āĻ)
- Square Root → Find the original number (āĻŦā§°ā§āĻāĻŽā§āĻ˛ → āĻŽā§āĻ˛ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ āĻŦāĻŋāĻāĻžā§°āĻ)