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Question

Mathematics Question on Square Roots of Decimals

Find the square root of each of the following numbers by division method.

  1. 2304
  2. 4489
  3. 3481
  4. 529
  5. 3249
  6. 1369
  7. 5776
  8. 7921
  9. 576
  10. 1024
  11. 3136
  12. 900
Answer

(i)The square root of 23042304 can be calculated as follows.

| 48
---|---
4| 2ˉ3ˉ0ˉ4ˉ\bar2\bar3\bar0\bar4
16-16
88| 704
704
| 0

2304=48\therefore\sqrt{2304}=48


(ii) The square root of 44894489 can be calculated as follows.

| 67
---|---
6| 4ˉ4ˉ8ˉ9ˉ\bar4\bar4\bar8\bar9
36-36
127| 889
889
| 0

4489=67\therefore \sqrt{4489}=67


(iii) The square root of 34813481 can be calculated as follows.

| 59
---|---
5| 3ˉ4ˉ8ˉ1ˉ\bar3\bar4\bar8\bar1
25-25
109| 981
981
| 0

3481=59\therefore\sqrt{3481}=59


(iv) The square root of 529529 can be calculated as follows.

| 23
---|---
2| 5ˉ2ˉ9ˉ\bar5\bar2\bar9
4-4
43| 129
129
| 0

529=23\therefore\sqrt{529}=23


(v) The square root of 32493249 can be calculated as follows.

| 57
---|---
5| 3ˉ2ˉ4ˉ9ˉ\bar3\bar2\bar4\bar9
25-25
107| 749
749
| 0

Hence, the square root of 32493249 is 5757.


(vi) 13691369

| 37
---|---
3| 1ˉ3ˉ6ˉ9ˉ\bar1\bar3\bar6\bar9
9-9
67| 469
-469
| 0

Hence, the square root of 13691369 is 3737.


(vii) 57765776

| 76
---|---
7| 5ˉ7ˉ7ˉ6ˉ\bar5\bar7\bar7\bar6
49-49
146| 876
-876
| 0

Hence, the square root of 57765776 is 7676.


(viii) 79217921

| 89
---|---
8| 7ˉ9ˉ2ˉ1ˉ\bar7\bar9\bar2\bar1
64-64
169| 1521
-1521
| 0

Hence, the square root of 79217921 is 8989


(ix) 576576

| 24
---|---
2| 5ˉ7ˉ6ˉ\bar5\bar7\bar6
4-4
44| 176
-176
| 0

Hence, the square root of 576576 is 2424.


(x) 10241024

| 32
---|---
3| 1ˉ0ˉ2ˉ4ˉ\bar1\bar0\bar2\bar4
9-9
62| 124
-124
| 0

Hence, the square root of 10241024 is 3232.


(xi) 31363136

| 56
---|---
5| 3ˉ1ˉ3ˉ6ˉ\bar3\bar1\bar3\bar6
25-25
106| 636
-636
| 0

Hence, the square root of 31363136 is 5656.


(xii) 900900

| 30
---|---
3| 9ˉ0ˉ0ˉ\bar9\bar0\bar0
9-9
00| 000
-000
| 0

Hence, the square root of 900900 is 3030.