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  • Last Modified 30-08-2022

NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots

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NCERT Solutions For Class 8 Maths Chapter 6: The students of CBSE Class 8 who are looking for NCERT Solutions for Mathematics Chapter 6 can find this article useful for them. Here we have provided all the solutions for the Square and Square Roots chapter. We found these solutions with the help of top academic experts at Embibe. Moreover, these solutions have been written in a simple and easy-to-understand language so that any class 8 student can easily get understand them.

CBSE Class 8 Maths Chapter 6 talks about the Properties of Square Numbers, Patterns in Numbers, Finding the Square of a Number and Square Roots. Embibe delivers a set of 470+ practice questions for all the sub-topics of Chapter 6. Students must emphasise practising all the in-text questions of Embibe to perform well in the exams. Keep reading to know NCERT solutions for Class 8, chapter 6 Maths.

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NCERT Solutions for Class 8 Maths Chapter 6: Important Topics

Squares and Square Roots chapter contains easy-to-solve problems. Students can go through the conceptual videos before solving the problems to arrive at the solutions easily. Students must practice various types of questions to know the steps involved and the right method of solving. It helps students to answer any kind of question asked in the exam.

Embibe delivers the solutions for every problem of the CBSE Class 8 Maths chapter 6 textbook by taking into consideration the latest syllabus. Students can access all the questions for free at Embibe to practice them and score good marks. Apart from free NCERT solutions, students can also access NCERT 3D Videos, NCERT Exemplars, Embibe Explainers, etc., for free.

We have mentioned the list of topics present in Class 8 Maths Chapter 6 as mentioned below:

S.NoTopic Name
1Properties of Square Numbers
2Patterns in Numbers
3Finding the Square of a Number
4Square Roots
5Square Roots of Decimals
6Estimating Square Root

NCERT Solutions for Class 8 Maths Chapter 6: Points to Remember

Some important points of Class 8 Maths Chapter 6 have been mentioned below. Students can make a note of them to revise them before final exams:

  •  Properties of Squares Numbers:
    (i) A number ending in 2, 3, 7,2, 3, 7, or 8 is never a perfect square.
    The number of zeroes in the end of a perfect square is never odd. So, a number ending in an odd number of zeroes is never a perfect square.
    (iii) Squares of even numbers are always even.
    (iv) Squares of odd numbers are always odd.
  • General Properties of Perfect Squares:
    (i) The square of a natural number other than 1 is either a multiple of 4 or exceeds a multiple of 4 by 1.
  • The square of a natural number other than 1, is either a multiple of 3 or exceeds a multiple of 3 by 1.
  • Finding Square Roots:
    (i) In order to find the square root of a perfect square, resolve it into prime factors; make pairs of similar factors and take the product of prime factors, choosing one out of every pair.
    (ii) For finding the square root of a decimal fraction, make the even number of decimal places by affixing a zero, if necessary; mark off periods and extract the square root; putting the decimal point in the square root as soon as the integral part is exhausted.

NCERT Solutions for Class 8 Maths: All Chapters

Students can find the detailed NCERT Class 8 Maths solutions for all the chapters as provided below for your reference:

FAQs on NCERT Solutions for Class 8 Maths Chapter 6

Q.1: The squares of which of the following would be odd numbers?
i. 431
ii. 2826
iii. 7779
iv. 82004
Ans: We know that the square of an odd number is odd and the square of an even number is even. So,
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.

Q.2: What will be the unit digit of the squares of the following numbers?
i. 81
ii. 272
iii. 799
iv. 3853
v. 1234

Ans: 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 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 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 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 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.

Q.3: The following numbers are obviously not perfect squares. Give reason.
i. 1057
ii. 23453
iii. 7928
iv. 222222
v. 64000

Ans: 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
Q,4: The squares of which of the following would be odd numbers?
i. 431
ii. 2826
iii. 7779
iv. 82004

Ans: Since 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.

Q.5: Without adding, find the sum.
i. 1 + 3 + 5 + 7 + 9
ii. 1 + 3 + 5 + 7 + 9 + I1 + 13 + 15 + 17 +19
iii. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Ans: i) Sum of first five odd number = (5)2 = 25
ii) Sum of first ten odd number = (10)2 = 100
iii) Sum of first thirteen odd number = (12)2 = 144

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