The NCERT solutions for Class 8 maths enhance topics with frequent, focused, engaging maths challenges and activities that strengthen maths concepts. Each question of the exercise has been carefully solved for the students to understand, keeping the examination point of view in mind.
Class 8 Maths Chapter 6 – Squares and Square Roots Exercise 6.1 questions and answers help students to understand the difference between squares and square roots, as well as how to find them out. These NCERT Solutions are prepared by subject experts at BYJU’S using a step-by-step approach.
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Exercise 6.4 Solutions 9 Questions
Access Answers of Maths NCERT Class 8 Chapter 6 – Squares and Square Roots Exercise 6.1 Page Number 96
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.
∴ The unit digit of the square of the number 81 is equal to 1.
ii. The unit digit of the square of a number having the digit 2 as the unit’s place is 4.
∴ The unit digit of the square of the number 272 is equal to 4.
iii. The unit digit of the square of a number having the digit 9 as the unit’s place is 1.
∴ The unit digit of the square of the number 799 is equal to 1.
iv. The unit digit of the square of a number having the digit 3 as the unit’s place is 9.
∴ The unit digit of the square of the number 3853 is equal to 9.
v. The unit digit of the square of a number having the digit 4 as the unit’s place is 6.
∴ The unit digit of the square of the number 1234 is equal to 6.
vi. The unit digit of the square of a number having the digit 7 as the unit’s place is 9.
∴ The unit digit of the square of the number 26387 is equal to 9.
vii. The unit digit of the square of a number having the digit 8 as the unit’s place is 4.
∴ The unit digit of the square of the number 52698 is equal to 4.
viii. The unit digit of the square of a number having the digit 0 as the unit’s place is 01.
∴ The unit digit of the square of the number 99880 is equal to 0.
ix. The unit digit of the square of a number having the digit 6 as the unit’s place is 6.
∴ The unit digit of the square of the number 12796 is equal to 6.
x. The unit digit of the square of a number having the digit 5 as the unit’s place is 5.
∴ The unit digit of the square of the 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
3. The squares of which of the following would be odd numbers?
i. 431
ii. 2826
iii. 7779
iv. 82004
Solution:
We know that the square of an odd number is odd, and the square of an even number is even.
i. The square of 431 is an odd number.
ii. The square of 2826 is an even number.
iii. The square of 7779 is an odd number.
iv. The square of 82004 is an even number.
4. Observe the following pattern and find the missing numbers. 112 = 121
1012 = 10201
10012 = 1002001
1000012 = 1 …….2………1
100000012 = ……………………..
Solution:
We observe that the square on the number on R.H.S of the equality has an odd number of digits such that the first and last digits both are 1 and the middle digit is 2. And the number of zeros between the left-most digit 1 and the middle digit 2 and the right-most digit 1 and the middle digit 2 is the same as the number of zeros in the given number.
∴ 1000012 = 10000200001
100000012 = 100000020000001
5. Observe the following pattern and supply the missing numbers. 112 = 121
1012 = 10201
101012 = 102030201
10101012 = ………………………
…………2 = 10203040504030201
Solution:
We observe that the square on the number on R.H.S of the equality has an odd number of digits such that the first and last digits both are 1. And the square is symmetric about the middle digit. If the middle digit is 4, the number to be squared is 10101, and its square is 102030201.
So, 10101012 =1020304030201
1010101012 =10203040505030201
6. Using the given pattern, find the missing numbers. 12 + 22 + 22 = 32
22 + 32 + 62 = 72
32 + 42 + 122 = 132
42 + 52 + _2 = 212
5 + _ 2 + 302 = 312
6 + 7 + _ 2 = _ 2
Solution:
Given, 12 + 22 + 22 = 32
i.e 12 + 22 + (1×2 )2 = ( 12 + 22 -1 × 2 )2
22 + 32 + 62 =72
∴ 22 + 32 + (2×3 )2 = (22 + 32 -2 × 3)2
32 + 42 + 122 = 132
∴ 32 + 42 + (3×4 )2 = (32 + 42 – 3 × 4)2
42 + 52 + (4×5 )2 = (42 + 52 – 4 × 5)2
∴ 42 + 52 + 202 = 212
52 + 62 + (5×6 )2 = (52+ 62 – 5 × 6)2
∴ 52 + 62 + 302 = 312
62 + 72 + (6×7 )2 = (62 + 72 – 6 × 7)2
∴ 62 + 72 + 422 = 432
7. Without adding, find the sum.
i. 1 + 3 + 5 + 7 + 9
Solution:
Sum of first five odd numbers = (5)2 = 25
ii. 1 + 3 + 5 + 7 + 9 + I1 + 13 + 15 + 17 +19
Solution:
Sum of first ten odd numbers = (10)2 = 100
iii. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
Solution:
Sum of first thirteen odd numbers = (12)2 = 144
8. (i) Express 49 as the sum of 7 odd numbers.
Solution:
We know that the sum of the first n odd natural numbers is n2 . Since,49 = 72
∴ 49 = sum of first 7 odd natural numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13
(ii) Express 121 as the sum of 11 odd numbers. Solution:
Since, 121 = 112
∴ 121 = sum of first 11 odd natural numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21
9. How many numbers lie between squares of the following numbers?
i. 12 and 13
ii. 25 and 26
iii. 99 and 100
Solution:
Between n2 and (n+1)2, there are 2n non–perfect square numbers.
i. 122 and 132, there are 2×12 = 24 natural numbers.
ii. 252 and 262, there are 2×25 = 50 natural numbers.
iii. 992 and 1002, there are 2×99 =198 natural numbers.
Exercise 6.1 of NCERT Solutions for Class 8 Maths Chapter 6- Squares and Square Roots is based on the following topics:
- Introduction to squares and square roots
- What are square numbers?
- Properties of Square Numbers
- Some interesting patterns
- Adding triangular numbers
- Numbers between square numbers
- Adding odd numbers
- A sum of consecutive natural numbers
FAQs
What is square and square roots Class 8? ›
Square root: The Square root of a number is a value that when multiplied by itself gives the original value. There are two methods two find the square root of the given number: Prime factorization method. Division method.
What is square in math class 8? ›Definition. Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.
What is a perfect square Class 8? ›A number is a perfect square or a square number if its square root is an integer, which means it is an integer's product with itself.
How to solve √ 81? ›Square Root of 81 by Prime Factorization Method
We know that the prime factorization of 81 is 3 × 3 × 3 × 3. √81 = 3×3 = 9. Hence, the value of the square root of 81 is 9.
For example, 6 × 6 = 36. Here, 36 is the square of 6. The square root of a number is that factor of the number and when it is multiplied by itself the result is the original number. Now, if we want to find the square root of 36, that is, √36, we get the answer as, √36 = 6.
How to solve √ 2? ›Root 2 is an irrational number as it cannot be expressed as a fraction and has an infinite number of decimals. So, the exact value of the root of 2 cannot be determined.
What are 4 types of square? ›A rectangle with two adjacent equal sides. A quadrilateral with four equal sides and four right angles. A parallelogram with one right angle and two adjacent equal sides. A rhombus with a right angle.
Is 5050 a perfect square? ›The numbers 257 and 5050 are not perfect squares.
What is the square of 8 answer? ›...
Square root Table From 1 to 15.
| Number | Squares | Square Root (Upto 3 places of decimal) |
|---|---|---|
| 7 | 72 = 49 | √7 = 2.646 |
| 8 | 82 = 64 | √8 = 2.828 |
| 9 | 92 = 81 | √9 = 3.000 |
| 10 | 102 = 100 | √10 = 3.162` |
The square root of 100 is 10. It is the positive solution of the equation x2 = 100. The number 100 is a perfect square.
How to solve √ 40? ›
The square root of 40 is symbolically expressed as √40. Thus, if we multiply the number 6.3245 two times, we get the original value 40. √40 = ± 6.3245. Square Root of 40 in Decimal Form: 6.3245.
How to solve √ 625? ›Square root of 625 is 25 and is represented as √625 = 25. A square root is an integer (can be either positive or negative) which when multiplied with itself, results in a positive integer called as the perfect square number.
Is 3.14 a square root? ›Because all square roots of irrational numbers are irrational numbers, the square root of pi is also an irrational number. However, that doesn't mean we can't approximate the answer. Just like we approximate the value of pi to be 3.14, we can approximate the square root of pi to be 1.77.
What is the square √ 64? ›The square root of 64 is 8, i.e. √64 = 8.
What is the formula of √? ›The square root of a number is a number squaring which gives the original number. It is that factor of the number that when squared gives the original number. It is the value of power 1/2 of that number. The square root of a number is represented as √.
What is a square in math? ›A square is a two-dimensional closed shape with 4 equal sides and 4 vertices. Its opposite sides are parallel to each other. We can also think of a square as a rectangle with equal length and breadth.
What is square example? ›Definition: A square is a two-dimensional shape which has four sides of equal length. The opposite sides of a square are parallel to each other and all four interior angles are right angles. Paper napkins, chess boards, cheese slices, floor tiles, and so on are some real-life examples of square shaped objects.
What meaning is square? ›a flat shape with four sides of equal length and four angles of 90°: First draw a square. It's a square-shaped room.
Why is 8 a square number? ›Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect square or simply “a square.” So, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.
How to find square root? ›- Square root of a number is a value, which on multiplication by itself, gives the original number. ...
- Suppose x is the square root of y, then it is represented as x=√y, or we can express the same equation as x2 = y.
What is a square root example? ›
A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16.
What is square formula? ›The Formula for the Area of A Square
The area of a square is equal to (side) × (side) square units. The area of a square when the diagonal, d, is given is d2÷2 square units. For example, The area of a square with each side 8 feet long is 8 × 8 or 64 square feet (ft2).
A square number is a number multiplied by itself. This can also be called 'a number squared'. The symbol for squared is ².
Why is it called a square? ›square (adj.) early 14c., "containing four equal sides and right angles," from square (n.), or from Old French esquarre, past participle of esquarrer. Meaning "honest, fair," is first attested 1560s; that of "straight, direct" is from 1804.