NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.3 Part 5
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Question: 6 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:
(i) 252
(ii) 2925
(iii) 396
(iv) 2645
(v) 2800
(vi) 1620
Answer:
(i) 252
2 | 252 |
2 | 126 |
3 | 63 |
3 | 21 |
7 | 7 |
1 |
Here, prime factor 7 has no pair.
Therefore 252 must be divided by 7 to make it a perfect square.
(ii) 2925
3 | 2925 |
3 | 975 |
5 | 325 |
5 | 65 |
13 | 13 |
1 |
Here, prime factor 13 has no pair.
Therefore 2925 must be divided by 13 to make it a perfect square.
(iii) 396
2 | 396 |
2 | 198 |
3 | 99 |
3 | 33 |
11 | 11 |
1 |
Here, prime factor 11 has no pair.
Therefore 396 must be divided by 11 to make it a perfect square.
(iv) 2645
5 | 2645 |
23 | 529 |
23 | 23 |
1 |
Here, prime factor 5 has no pair.
Therefore 2645 must be divided by 5 to make it a perfect square.
(v) 2800
2 | 2800 |
2 | 1400 |
2 | 700 |
2 | 350 |
5 | 175 |
5 | 35 |
7 | 7 |
1 |
Here, prime factor 7 has no pair.
Therefore 2800 must be divided by 7 to make it a perfect square.
And
(vi) 1620
2 | 1620 |
2 | 810 |
3 | 405 |
3 | 135 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Here, prime factor 5 has no pair.
Therefore 1620 must be divided by 5 to make it a perfect square.
And