PPT: A Square and A Cube | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

 Page 1


A SQUARE AND A CUBE
Page 2


A SQUARE AND A CUBE
What is a Square Number?
A square number is what we get when we multiply a 
number by itself.
We write it as n × n = n²
For example:
1 × 1 = 1² = 1
2 × 2 = 2² = 4
3 × 3 = 3² = 9
4 × 4 = 4² = 16
5 × 5 = 5² = 25
Square numbers are called "squares" because they 
represent the area of a square!
Page 3


A SQUARE AND A CUBE
What is a Square Number?
A square number is what we get when we multiply a 
number by itself.
We write it as n × n = n²
For example:
1 × 1 = 1² = 1
2 × 2 = 2² = 4
3 × 3 = 3² = 9
4 × 4 = 4² = 16
5 × 5 = 5² = 25
Square numbers are called "squares" because they 
represent the area of a square!
Patterns in Square Numbers
Last Digits
Square numbers only end with 
these digits:
0, 1, 4, 5, 6, or 9
They never end with 2, 3, 7, or 
8.
Zeros at the End
If a number ends with zeros, 
its square will have twice as 
many zeros at the end.
Example: 100² = 10,000
Even and Odd
The square of an even number 
is always even.
The square of an odd number 
is always odd.
Page 4


A SQUARE AND A CUBE
What is a Square Number?
A square number is what we get when we multiply a 
number by itself.
We write it as n × n = n²
For example:
1 × 1 = 1² = 1
2 × 2 = 2² = 4
3 × 3 = 3² = 9
4 × 4 = 4² = 16
5 × 5 = 5² = 25
Square numbers are called "squares" because they 
represent the area of a square!
Patterns in Square Numbers
Last Digits
Square numbers only end with 
these digits:
0, 1, 4, 5, 6, or 9
They never end with 2, 3, 7, or 
8.
Zeros at the End
If a number ends with zeros, 
its square will have twice as 
many zeros at the end.
Example: 100² = 10,000
Even and Odd
The square of an even number 
is always even.
The square of an odd number 
is always odd.
Squares and Odd Numbers
There's a fascinating pattern between square 
numbers and odd numbers:
1 = 1 = 1²
1 + 3 = 4 = 2²
1 + 3 + 5 = 9 = 3²
1 + 3 + 5 + 7 = 16 = 4²
1 + 3 + 5 + 7 + 9 = 25 = 5²
Every square number can be expressed as the sum 
of consecutive odd numbers starting from 1!
This pattern can be visualized by adding L-shaped 
layers around a central point, where each new layer 
represents the next odd number.
Page 5


A SQUARE AND A CUBE
What is a Square Number?
A square number is what we get when we multiply a 
number by itself.
We write it as n × n = n²
For example:
1 × 1 = 1² = 1
2 × 2 = 2² = 4
3 × 3 = 3² = 9
4 × 4 = 4² = 16
5 × 5 = 5² = 25
Square numbers are called "squares" because they 
represent the area of a square!
Patterns in Square Numbers
Last Digits
Square numbers only end with 
these digits:
0, 1, 4, 5, 6, or 9
They never end with 2, 3, 7, or 
8.
Zeros at the End
If a number ends with zeros, 
its square will have twice as 
many zeros at the end.
Example: 100² = 10,000
Even and Odd
The square of an even number 
is always even.
The square of an odd number 
is always odd.
Squares and Odd Numbers
There's a fascinating pattern between square 
numbers and odd numbers:
1 = 1 = 1²
1 + 3 = 4 = 2²
1 + 3 + 5 = 9 = 3²
1 + 3 + 5 + 7 = 16 = 4²
1 + 3 + 5 + 7 + 9 = 25 = 5²
Every square number can be expressed as the sum 
of consecutive odd numbers starting from 1!
This pattern can be visualized by adding L-shaped 
layers around a central point, where each new layer 
represents the next odd number.
Square Roots
The square root is the inverse operation of squaring a number. It answers the question: "What number, when 
multiplied by itself, gives this result?"
1
Finding Square Roots
The square root of 49 is 7 because 7 × 7 = 49
We write this as: :49 = 7
2
Positive and Negative
Every positive number has two square roots - one positive and one negative.
For example, :64 = 8 or -8 (because 8² = 64 and (-8)² = 64)
3
Perfect Squares
Numbers like 1, 4, 9, 16, 25... have whole number square roots.
Other numbers have square roots that are not whole numbers.