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NCERT Class 8 Maths Textbook Chapter 6 With Answer Book PDF Free Download
Chapter 6:Squares And Square Roots
6.1 Introduction
You know that the area of a square = side × side (where ‘side’ means ‘the length of a side).
Study the following table.
Side of a square (in cm) Area of the square (in cm2)
1 1 × 1 = 1 = 12
2 2 × 2 = 4 = 22
3 3 × 3 = 9 = 32
5 5 × 5 = 25 = 52
8 8 × 8 = 64 = 82
a a × a = a2
What is special about the numbers 4, 9, 25, 64, and other such numbers?
Since 4 can be expressed as 2 × 2 = 22
, 9 can be expressed as 3 × 3 = 32, all such
numbers can be expressed as the product of the number with itself. Such numbers like 1, 4, 9, 16, 25, … are known as square numbers.
In general, if a natural number m can be expressed as n2, where n is also a natural number, then m is a square number. Is 32 a square number?
We know that 52
= 25 and 62
= 36.
If 32 is a square number, it must be the square of a natural number between 5 and 6. But there is no natural number between 5 and 6. Therefore 32 is not a square number. Consider the following numbers and their squares
| Author | NCERT |
| Language | English |
| No. of Pages | 20 |
| PDF Size | 278 KB |
| Category | Mathematics |
| Source/ Credits | ncert.nic.in |
NCERT Solutions Class 8 Maths Chapter 6 Squares And Square Roots
1. What will be the unit digit of the squares of the following numbers?
i. 81
ii. 272
iii. 799
iv. 3853
v. 1234
vi. 26387
vii. 52698
viii. 99880
ix. 12796
x. 55555
Solution:
The unit digit of the square of a number having ‘a’ at its unit place ends with a×a.
i. The unit digit of the square of a number having digit 1 as the unit’s place is 1.
∴ Unit digit of the square of number 81 is equal to 1.
ii. The unit digit of the square of a number having digit 2 as the unit’s place is 4.
∴ Unit digit of the square of the number 272 is equal to 4.
iii. The unit digit of the square of a number having digit 9 as the unit’s place is 1.
∴ Unit digit of the square of number 799 is equal to 1.
iv. The unit digit of the square of a number having digit 3 as the unit’s place is 9.
∴ Unit digit of the square of number 3853 is equal to 9.
v. The unit digit of the square of a number having digit 4 as unit’s place is 6.
∴ Unit digit of the square of number 1234 is equal to 6.
vi. The unit digit of the square of a number having digit 7 as unit’s place is 9.
∴ Unit digit of the square of number 26387 is equal to 9.
vii. The unit digit of the square of a number having digit 8 as unit’s place is 4.
∴ Unit digit of the square of number 52698 is equal to 4.
viii. The unit digit of the square of a number having digit 0 as unit’s place is 01.
∴ Unit digit of the square of the number 99880 is equal to 0.
ix. The unit digit of the square of a number having digit 6 as unit’s place is 6.
∴ Unit digit of the square of number 12796 is equal to 6.
x. The unit digit of the square of a number having digit 5 as unit’s place is 5.
∴ Unit digit of the square of number 55555 is equal to 5.
2. The following numbers are obviously not perfect squares. Give reason.
i. 1057
ii. 23453
iii. 7928
iv. 222222
v. 64000
vi. 89722
vii. 222000
viii. 505050
Solution:
We know that natural numbers ending in the digits 0, 2, 3, 7, and 8 are not perfect squares.
i. 1057 ⟹ Ends with 7
ii. 23453 ⟹ Ends with 3
iii. 7928 ⟹ Ends with 8
iv. 222222 ⟹ Ends with 2
v. 64000 ⟹ Ends with 0
vi. 89722 ⟹ Ends with 2
vii. 222000 ⟹ Ends with 0
viii. 505050 ⟹ Ends with 0
NCERT Class 8 Maths Textbook Chapter 6 With Answer Book PDF Free Download