## NCERT Solutions for Class 8 Chapter 6 Squares and Square Roots -Free PDF Download

Free PDF download of NCERT Solutions Maths Class 8 Solutions Chapter 6 – Squares and Square Roots solved by Expert Maths Teachers on CoolGyan.Org. All Chapter 6 – Squares and Square Roots Questions with Solutions for NCERT to help you to revise complete Syllabus and Score More marks.

Maths Revision Notes for Class 8

Chapter Name | Squares and Square Roots |

Chapter | Chapter 6 |

Exercise | Exercise 6.1 |

Class | Class 8 |

Subject | Maths NCERT Solutions |

Board | CBSE |

TEXTBOOK | CBSE NCERT |

Category | NCERT Solutions |

**NCERT SOLVED**

**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**

**Ans. (i)** The number 81 contains its unit’s place digit 1. So, square of 1 is 1.

Hence, unit’s digit of square of 81 is 1.

**(ii)** The number 272 contains its unit’s place digit 2. So, square of 2 is 4.

Hence, unit’s digit of square of 272 is 4.

**(iii)** The number 799 contains its unit’s place digit 9. So, square of 9 is 81.

Hence, unit’s digit of square of 799 is 1.

**(iv)** The number 3853 contains its unit’s place digit 3. So, square of 3 is 9.

Hence, unit’s digit of square of 3853 is 9.

**(v)** The number 1234 contains its unit’s place digit 4. So, square of 4 is 16.

Hence, unit’s digit of square of 1234 is 6.

**(vi)** The number 26387 contains its unit’s place digit 7. So, square of 7 is 49.

Hence, unit’s digit of square of 26387 is 9.

**(vii)** The number 52698 contains its unit’s place digit 8. So, square of 8 is 64.

Hence, unit’s digit of square of 52698 is 4.

**(viii)** The number 99880 contains its unit’s place digit 0. So, square of 0 is 0.

Hence, unit’s digit of square of 99880 is 0.

**(ix)** The number 12796 contains its unit’s place digit 6. So, square of 6 is 36.

Hence, unit’s digit of square of 12796 is 6.

**(x)** The number 55555 contains its unit’s place digit 5. So, square of 5 is 25.

Hence, unit’s digit of square of 55555 is 5.

**2. The following numbers are obviously not perfect squares. Give reasons.**

**(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 **

**(v) 64000 (vi) 89722 (vii) 222000 (viii) 505050**

**Ans. (i)** Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9. Therefore 1057 is not a perfect square because its unit’s place digit is 7.

**(ii)** Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9. Therefore 23453 is not a perfect square because its unit’s place digit is 3.

**(iii)** Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9.Therefore 7928 is not a perfect square because its unit’s place digit is 8.

**(iv)** Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9. Therefore 222222 is not a perfect square because its unit’s place digit is 2.

**(v)** Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9. Therefore 64000 is not a perfect square because its unit’s place digit is single 0.

**(vi)** Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9. Therefore 89722 is not a perfect square because its unit’s place digit is 2.

**(vii)** Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9. Therefore 222000 is not a perfect square because its unit’s place digit is triple 0.

**(viii)** Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9. Therefore 505050 is not a perfect square because its unit’s place digit is 0.

**3. The squares of which of the following would be odd number:**

**(i) 431 (ii) 2826 (iii) 7779 (iv) 82004**

**Ans**. **(i)** 431 – Unit’s digit of given number is 1 and square of 1 is 1. Therefore, square of 431 would be an odd number.

**(ii)** 2826 – Unit’s digit of given number is 6 and square of 6 is 36. Therefore, square of 2826 would not be an odd number.

**(iii)** 7779 – Unit’s digit of given number is 9 and square of 9 is 81. Therefore, square of 7779 would be an odd number.

**(iv)** 82004 – Unit’s digit of given number is 4 and square of 4 is 16. Therefore, square of 82004 would not be an odd number.

**4. Observe the following pattern and find the missing digits:**

** = 121**

** = 10201**

** = 1002001**

** = 1…….2…….1**

**100000012100000012 = 1……………………**

**Ans. ** = 121

= 10201

= 1002001

= 10000200001

**100000012100000012=100000020000001**

**5. Observe the following pattern and supply the missing numbers:**

** = 121**

** = 10201**

** = 102030201**

** = ………………………**

**= 10203040504030201**

**Ans. **= 121

= 10201

= 102030201

= 1020304030201

= 10203040504030201

**6. Using the given pattern, find the missing numbers:**

**Ans. **

**7. Without adding, find the sum:**

**(i) 1 + 3 + 5 + 7 + 9**

**(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19**

**(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23**

**Ans. **(i) Here, there are five odd numbers. Therefore square of 5 is 25.

1 + 3 + 5 + 7 + 9 = = 25

(ii) Here, there are ten odd numbers. Therefore square of 10 is 100.

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = = 100

(iii) Here, there are twelve odd numbers. Therefore square of 12 is 144.

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 = = 144

**8. (i) Express 49 as the sum of 7 odd numbers.**

**(ii) Express 121 as the sum of 11 odd numbers.**

**Ans. **(i) 49 is the square of 7. Therefore it is the sum of 7 odd numbers.

49 = 1 + 3 + 5 + 7 + 9 + 11 + 13

(ii) 121 is the square of 11. Therefore it is the sum of 11 odd numbers

121 = 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**

**Ans. (i)** Since, non-perfect square numbers between and are

Here, = 12

Therefore, non-perfect square numbers between 12 and 13 = = = 24

(i.e 132132– 122122– 1 =169 -144-1 = 25-1=24)

**(ii)** Since, non-perfect square numbers between and are

Here, = 25

Therefore, non-perfect square numbers between 25 and 26 = = = 50

(i.e 262262– 252252 – 1 =676 – 625-1 = 51-1=50)

**(iii)** Since, non-perfect square numbers between and are

Here, = 99

Therefore, non-perfect square numbers between 99 and 100 = = = 198

(i.e 10021002– 992992 – 1 =10000-9801-1 = 199-1=198)