6. For each of the following numbers, find the smallest whole number by which it should
W 1458
Vi 768
be divided so as to get a perfect square. Also find the square root of the square
number so obtained.
6) 252
(ii) 2925
(v) 2800
– (vi) 1620
(iv) 2645
(iii) 396
Answer:
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Answer 1. 1458 = 2 x 3 x 3 x 3 x 3 x 3 x 3
Here, prime factor 2 has no pair. Therefore 1458 must be multiplied by 2 to make it a perfect square.
\therefore1458\times2=2916∴1458×2=2916
And \sqrt{2916}=2\times3\times3\times3=54
2916
=2×3×3×3=54
2. 768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
Here, prime factor 3 has no pair. Tehrefore 768 must be multiplied by 3 to make it a perfect square.
\therefore768\times3=2304∴768×3=2304
And \sqrt{2304}=2\times2\times2\times2\times3=48
2304
=2×2×2×2×3=48
Therefore 252 must be divided by 7 to make it a perfect square. Here, prime factor 13 has no pair. Therefore 2925 must be divided by 13 to make it a perfect square. Here, prime factor 11 has no pair.