Square Roots
Exercise 6.4
Part 1
Question 1: Find the square root of each of the following numbers by Division method.
(i) 2304
4 4 | 2304 16 | 48 |
88 8 | 704 704 | |
0 |
`sqrt(2304)=48`
(ii) 4489
6 6 | 4489 36 | 67 |
127 7 | 889 889 | |
0 |
`sqrt(4489)=67`
(iii) 529
2 2 | 529 4 | 23 |
43 | 129 129 | |
9 |
`sqrt(529)=23`
(iv) 3249
5 5 | 3249 25 | 57 |
107 7 | 749 749 | |
0 |
`sqrt(3249)=57`
(v) 1369
3 3 | 1369 9 | 37 |
67 7 | 469 469 | |
0 |
`sqrt(1369)=37`
(vi) 5776
7 7 | 5776 49 | 76 |
146 6 | 876 876 | |
0 |
`sqrt(5776)=76`
(vii) 7921
8 8 | 7921 64 | 89 |
169 9 | 1521 1521 | |
0 |
`sqrt(7921)=89`
(viii) 576
2 2 | 576 4 | 24 |
44 4 | 176 176 | |
0 |
`sqrt(576)=24`
(ix) 1024
3 3 | 1024 9 | 32 |
62 2 | 124 124 | |
0 |
`sqrt(1024)=32`
(x) 3136
5 5 | 3136 25 | 56 |
106 6 | 636 636 | |
0 |
`sqrt(3136)=56`
(xi) 900
3 3 | 900 9 | 30 |
60 0 | 000 000 | |
0 |
`sqrt(900)=30`
Question 2: Find the number of digits in the square root of each of the following numbers (without any calculation).
(i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625
Answer: If there are even number of digits in square then number of digits in
Square Root `=(π)/(2)`
If there are odd number of digits in square then number of digits in
Square Root `=(π+1)/(2)`
(i) 1, (ii) 2, (iii) 2, (iv) 3, (v) 3
3. Find the square root of the following decimal numbers.
(i) 2.56
1 1 | 2.56 1 | 1.6 |
26 6 | 156 156 | |
0 |
`sqrt(2.56)=1.6`
(ii) 7.29
2 2 | 7.29 4 | 2.7 |
47 7 | 329 329 | |
0 |
`sqrt(7.29)=2.7`
(iii) 51.84
7 7 | 51.84 49 | 7.2 |
142 2 | 284 284 | |
0 |
`sqrt(51.84)=7.2`
(iv) 42.25
6 6 | 42.25 36 | 6.5 |
125 5 | 625 625 | |
0 |
`sqrt(42.25=6.5`
(v) 31.36
5 5 | 31.36 25 | 5.6 |
106 6 | 636 636 | |
0 |
`sqrt(31.36)=5.6`