Question

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Answer 1

Step-by-step explanation:

if a number has 1 or 9 in the unit’s place, then it’s square ends in 1.

when a square number ends in 6, the number whose square it is, will have either 4 or 6 in unit’s place

when a square number ends in 9, the number whose square it is, will have either 3 or 7 in unit’s place

when a square number ends in5, the number whose square it is, will have 5 in unit’s place

when a square number ends in 4, the number whose square it is, will have either 2 or 8 in unit’s place

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Solution:

1)  1 and 9.

Since 1² and 9² give 1 at unit’s place, so these are the possible values of unit digit of the square root.

2)  4 and 6

Since, 4²=16 and 6² = 36, hence, 4 and 6 are possible digits

3) 1 and 9

Since 1² and 9² give 1 at unit’s place, so these are the possible values of unit digit of the square root.

 

4) 5

Since, 5²= 25, hence 5 is possible.

If the units digit of a number is 2, 3, 7 or 8 then it is not a perfect square and hence does not have a square root.

 (2.)

If a number has a square root then its units digit must be 0, 1, 4, 5, 6 or 9.

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Solution:

(i)153           (ii) 257           (iii) 408 are not perfect squares

Since, (i), (ii) and (iii) are surely not be perfect square as these numbers end with 3, 7 and 8.

3)

Square root by repeated subtraction:

This is the simplest method of finding the square root of a perfect square. It works very well for small numbers.

Take the number n whose square root is required . Subtract from and the odd numbers 1, 3, 5 7, 9….. successively . If n is a perfect square we will get zero at some stage . We stop at this point and declared the number of times we have perform subtraction as the square root of n.

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 Solution:

√100 by Repeated subtraction:

1. 100 - 1 = 99

2. 99 - 3 = 96

3. 96 - 5 = 91

4. 91 -7 = 84

5. 84 - 9 = 75

6. 75 - 11 = 64

7. 64 - 13 = 51

8. 51 - 15 = 36

9. 36-17=19

10. 19 - 19 = 0

We get 0 at 10th step. Hence,10 is the square root of 100.

√100 = 10

√169 by Repeated subtraction:

1. 169 - 1 = 168

2. 168 - 3 = 165

3. 165 - 5 = 160

4. 160 - 7 = 153

5. 153 - 9 = 144

6. 144 - 11 = 133

7. 133 - 13 = 120

8. 120 - 15 = 105

9. 105 - 17 = 88

10. 88 - 19 = 69

11. 69 - 21 = 48

12. 48 - 23 = 25

13. 25 - 25 = 0

We get 0 at 13th step. Hence,13 is the square root of 169

 √169=13

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Answer 2

Answer:

Question 1

The possible digit at one's place of the square root of:

(i) 9801 can be 1 or 9.

(ii) 99856 Can be 4 or 6

( iii) 998001 can be 1 or 9

( iv) 657666025 can be 5

Question 2

1. (i)153
2. (ii) 257
3. (iii) 408 are not perfect squares

Since, (i), (ii) and (iii) are surely not be perfect square as these numbers end with 3, 7 and 8.

Question 3

100-1=99

100-1=9999-3=96

100-1=9999-3=9696-5=91

100-1=9999-3=9696-5=9191-7=84

100-1=9999-3=9696-5=9191-7=8484-9=75

100-1=9999-3=9696-5=9191-7=8484-9=7575-11=64

100-1=9999-3=9696-5=9191-7=8484-9=7575-11=6464-13=51

100-1=9999-3=9696-5=9191-7=8484-9=7575-11=6464-13=5151-15=36

100-1=9999-3=9696-5=9191-7=8484-9=7575-11=6464-13=5151-15=3636-17=19

100-1=9999-3=9696-5=9191-7=8484-9=7575-11=6464-13=5151-15=3636-17=1919-19=0

100-1=9999-3=9696-5=9191-7=8484-9=7575-11=6464-13=5151-15=3636-17=1919-19=0√100=10

Question 4

Answer is in the attachment

Step-by-step explanation:

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