Question

check whether the given number are perfect square or not if not then find the smallest number by which the given number must be multiplied so as to get a perfect square in each case . 648, 1014, 6728, 1452, 2925, 22050​

Answer 1

a) 648 b) 1014

2 | 648 2 | 1014

2 | 324 3 | 507

2 | 162 13 | 169

2 | 81 13 | 13

3 | 27 1

3 | 9

3 | 3

1

= 2×2×2×3×3×3×3 = 2×3×13×13

= 648 × 2 = 1014 × 2 × 3

= 1296 = 6084

= √1296 = 36 = √6084 = 78

c) 6728 d) 1452

2 | 6728 2 | 1452

2 | 3364 2 | 726

2 | 1682 3 | 363

29 | 841 11 | 121

29 | 29 11 | 11

1 1

= 2×2×2×29×29 = 2×2×3×11×11

= 6728 × 2 = 1452 × 3

= 13456 = 4356

= √13456 = 116. = √4356 = 66

e) 2925 f) 22050

5 | 2925 2 | 22050

5 | 585 3 | 11025

3 | 117 3 | 3675

3 | 39 5 | 1225

13 | 13 5 | 245

1 7 | 49

7 | 7

= 5×5×3×3×13 1

= 2925 × 13

= 38025 = 2×3×3×5×5×7×7

= √38025 = 195 = 22050 × 2

= 44100

= √44100 = 210