Saved Bookmarks
| 1. |
By what number should each of the following numbers by multiplied to get a perfect square in each case? Also find the number whose square is the new number.(i) 8820(ii) 3675(iii) 605(iv) 2880 |
|
Answer» (i) 8820 The prime factors for 8820 =8820 = 2×2×3×3×7×7×5 (grouping the prime factors in equal pairs we get) = (2×2) × (3×3) × (7×7) × 5 Here,prime factor 5 is left out. So, multiply by 5 we get, = 8820 × 5 = (2×2) × (3×3) × (7×7) × (5×5) = (2×3×7×5) × (2×3×7×5) = 210 × 210 = (210)2 (ii) 3675 The prime factors for 3675 3675 = 5×5×7×7×3 (grouping the prime factors in equal pairs we get) = (5×5) × (7×7) × 3 Here,prime factor 3 is left out.So, multiply by 3 we get, = 3675 × 3 = (5×5) × (7×7) × (3×3) = (5×7×3) × (5×7×3) = 105 × 105 = (105)2 (iii) 605 The prime factors for 605 605 = 5×11×11 (grouping the prime factors in equal pairs we get) = (11×11) × 5 Here, prime factor 5 is left out.So, multiply by 5 we get, = 605 × 5 = (11×11) × (5×5) = (11×5) × (11×5) = 55 × 55 = (55)2 (iv) 2880 The prime factors for 2880 2880 = 5×3×3×2×2×2×2×2×2 (grouping the prime factors in equal pairs we get) = (3×3) × (2×2) × (2×2) × (2×2) × 5 Here, prime factor 5 is left out. So, multiply by 5 we get, = 2880 × 5 = (3×3) × (2×2) × (2×2) × (2×2) × (5×5) = (3×2×2×2×5) × (3×2×2×2×5) = 120 × 120 = (120)2 |
|