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

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

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

	67
6	\(\bar4\bar4\bar8\bar9\) \(-36\)
127	889 889
	0

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

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

	59
5	\(\bar3\bar4\bar8\bar1\) \(-25\)
109	981 981
	0

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

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

	23
2	\(\bar5\bar2\bar9\) \(-4\)
43	129 129
	0

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

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(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 \(30\).