For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained. 252 (ü) 2925 M 2800 (vi) 1620 (iv) 2645 fin396 The students of Class VIII of a school donated 2401 in all, for Prime Minister's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of studenti
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Answer:
i) 252=
2×2
×
3×3
×7
Therefore, we need to divide 252 by 7 in order to make it a perfect square.
So,
7
252
=36
∴
36
=6
ii) 2925=
3×3
×
5×5
×13
Therefore, we need to divide 2925 by 13 in order to make it a perfect square.
So,
13
2925
=225
∴
225
=15
iii) 396=
2×2
×
3×3
×11
Therefore, we need to divide 396 by 11 in order to make it a perfect square.
So,
11
396
=36
∴
36
=6
iv) 2645=
23×23
×5
Therefore, we need to divide 2645 by 5 in order to make it a perfect square.
So,
5
2645
=529
∴
529
=23
v) 2800=
2×2
×
2×2
×
5×5
×7
Therefore, we need to divide 2800 by 7 in order to make it a perfect square.
So,
7
2800
=400
∴
400
=20
vi) 1620=
2×2
×
3×3
×
3×3
×5
Therefore, we need to divide 1620 by 5 in order to make it a perfect square.
So,
5
1620
=324
∴
324
=18
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