Unit (2)
Square & Square Roots
SquarE & Square Root
• Squares are the numbers, generated after multiplying a value by itself.
• Whereas square root of a number is value which on getting multiplied by itself gives the
original value.
• Squares and square roots both concepts are opposite in nature to each other.
• Hence, both are vice-versa methods.
For example, the square of 2 is 4 and the square root of 4 is 2.
Properties of Square Numbers
The square numbers are the values which are produced when we
multiply a number by itself.
• Square of 1 is equal to 1
• Square of 0 is equal to 0
Square
Numbers
1 to 20
12 = 1
112 = 121
22 = 4
122 = 144
32 = 9
132 = 169
42 = 16
142 = 196
2
15 = 225
2
16 = 256
2
17 = 289
2
18 = 324
9 = 81
2
19 = 361
2
20 = 400
5 = 25
• Square of positive numbers are positive in nature
6 = 36
• Square of negative numbers are positive
7 = 49
For example, (-3)2 = 9
8 = 64
10 = 100
2
2
2
2
2
2
Square Roots of Number
Perfect
Square
Square
Root
• The square root of any number is the value which when multiplied by itself
gives the original number.
• It is denoted by the symbol, ‘√’.
• Squares and square roots both concepts are opposite in nature to each
other.
• Hence, both are inverse operations (or) vice-versa methods.
For example, the square of 2 is 4 and the square root of 4 is 2.
Let’s Learn
happily!
https://youtu.be/
cuAo3_54m1I
https://youtu.be/0cdrp
TxFkDU
Perfect squares song(Helps with memorizing
perfect squares)
Perfect Squares SongAceon Academy
https://youtu.be/
Mg5RSkhqQuI
Memorizing Squares by
Association - First 25 Quick Mental Math Trick
https://youtube.com/watch?v=
B4zejSI8zho&feature=share
Math Antics - Exponents and Square
Roots
https://youtube.com/watch?v=Yqgg3qMNvE&feature=share
THE SQUARE ROOT
🚀 What is the Square Root? 👨🏻🚀
Math for Kids
Practice
Squares and Square Roots (Explained)
(byjus.com)
Questions on Squares and square roots
Q1 What are squares and square roots?
• Square numbers are the numbers which are produced when a value is multiplied by
itself.
For example, the square of 10 is 102 = 10 x 10 = 100.
• The square root of a number is a value which on multiplied by itself gives the original
number. It is represented by the symbol ‘√’. For example, the square root of 25 is √25 =
5.
Q2 : What are perfect squares? Give an example
• Perfect squares are the numbers, the square root of which gives a whole number. For
example, 9 is a perfect square, because its root is a whole number, i.e.√9 = 3.
Q3 : What is an imperfect square with examples?
An imperfect square is a number, the square root of which gives a
fraction.
The value generated by taking the square root of the imperfect
square could be non-terminating as well.
For example, 3 is an imperfect square, because its root is equal to,
√3 = 1.73205080757, which is a fraction.
• Q4 : How to find the square root?
• To find the square root of a number we can use the prime
factorisation method. For example, the square root of 900 is:
• √900 = √(2 x 2 x 3 x 3 x 5 x 5 )
• Taking out the numbers in pairs, we get;
• √900 = 2 x 3 x 5 = 30
• 900 was a perfect square, but to find the root of an imperfect
square, we have to use long division method.
• Q5 :What is the difference between a square and square
roots?
• The square root of a number gives the root of a number which was
squared. This is the primary difference between them.