Question

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 1

(i)The square root of $2304$ can be calculated as follows.

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

$\therefore\sqrt{2304}=48$

---

(ii) The square root of $4489$ can be calculated as follows.

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

$\therefore \sqrt{4489}=67$

---

(iii) The square root of $3481$ can be calculated as follows.

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

$\therefore\sqrt{3481}=59$

---

(iv) The square root of $529$ can be calculated as follows.

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

$\therefore\sqrt{529}=23$

---

(v) The square root of $3249$ can be calculated as follows.

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

Hence, the square root of $3249$ is $57$.

---

(vi) $1369$

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

Hence, the square root of $1369$ is $37$.

---

(vii) $5776$

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

Hence, the square root of $5776$ is $76$.

---

(viii) $7921$

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

Hence, the square root of $7921$ is $89$

---

(ix) $576$

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

Hence, the square root of $576$ is $24$.

---

(x) $1024$

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

Hence, the square root of $1024$ is $32$.

---

(xi) $3136$

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

Hence, the square root of $3136$ is $56$.

---

(xii) $900$

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

Hence, the square root of $900$ is $30$.