- Square Number
- How to find the square of Number easily
- |
- Pythagorean triplets
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- Square Root
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- How to Find Square root
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- Estimating Digits in the Square Root

In this page we have *NCERT Solutions for Class 8 Maths Chapter 6 :Square roots * for
EXERCISE 1 . Hope you like them and do not forget to like , social share
and comment at the end of the page.

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

1 |
1 Explanation: Since, 1 ^{2} =1 |

2 |
4 Explanation: Since, 2 ^{2} = 4, |

3 |
1 Explanation: Since, 9 ^{2} = 81 |

4 |
9 Explanation: Since 3 ^{2} = 9 |

5 |
6 Explanation: Since, 4 ^{2} = 16 |

6 |
9 Explanation: Since, 7 ^{2} = 49 |

7 |
4 Explanation: Since, 8 ^{2} = 64. So |

8 |
0 Since, 0 ^{2} = 0. |

9 |
6 Explanation: Since, 6 ^{2} = 36 |

10 |
5 Explanation: Since, 5 ^{2} = 25 |

The following numbers are obviously not perfect squares. Give reason.

- 1057
- 23453
- 7928
- 222222
- 64000
- 89722
- 222000
- 505050

So (i), (ii), (iii), (iv), (vi) don’t have any of the 0, 1, 4, 5, 6, or 9 at unit’s place, so they are not be perfect squares.

So (v), (vii) and (viii) don’t have even number of zeroes at the end so they are not perfect squares.

The squares of which of the following would be odd numbers?

- 431
- 2826
- 7779
- 82004

- 431 square will end in 1,So odd number
- 2826 square will end in 6 ,so even number
- 779 square will end in 1,So odd number
- 82004 square will end in 6 ,so even number

Observe the following pattern and find the missing digits.

11

101

1001

100001

10000001

100001

10000001

Observe the following pattern and supply the missing numbers.

11

101

10101

1010101

..............

1010101

101010101

Using the given pattern, find the missing numbers.

1

2

3

4

5

6

Relation among first, second and third number - Third number is the product of first and second number

Relation between third and fourth number - Fourth number is 1 more than the third number

4

5

6

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

Explanation:

1 + 3 = 2

1 + 3 + 5 = 3

1 + 3 + 5 + 7 = 4

1 + 3 + 5 + 7 + 9 = 5

So Sum of n odd numbers starting from 1 = n

From the above derivation we can answer the above questions

- Since, there are 5 consecutive odd numbers, Thus, their sum = 5
^{2}= 25 - Since, there are 10 consecutive odd numbers, Thus, their sum = 10
^{2}= 100 - Since, there are 12 consecutive odd numbers, Thus, their sum = 12
^{2}= 144

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

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

Explanation:

1 + 3 = 2

1 + 3 + 5 = 3

1 + 3 + 5 + 7 = 4

1 + 3 + 5 + 7 + 9 = 5

So Sum of n odd numbers starting from 1 = n

1) Since, 49 = 7

So, 7

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

2) Since, 121 = 11

Therefore, 121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

How many numbers lie between squares of the following numbers?

(i) 12 and 13

(ii) 25 and 26

(iii) 99 and 100

1) 12

13

Now, 169 - 144 = 25

So, there are 25 - 1 = 24 numbers lying between 12

2) We know that, 25

And, 26

Now, 676 - 625 = 51

So, there are 51 - 1 = 50 numbers lying between 25

3) We know that, 99

And, 100

Now, 10000 - 9801 = 199

So, there are 199 - 1 = 198 numbers lying between 99

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