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By what least number should the given number be multiplied to get a perfect square number? In each case, find the number whose square is the new number.(i) 3675 (ii) 2156 (iii) 3332 (iv) 2925 |
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Answer» (i) 3675 At first, We’ll resolve the given number into prime factors: Hence, 3675 = 3 × 25 × 49 = 7 × 7 × 3 × 5 × 5 = (5 × 7) × (5 × 7) × 3 In the above factors only 3 is unpaired So, in order to get a perfect square the given number should be multiplied by 3 Hence, The number whose perfect square is the new number is as following: = (5 × 7) × (5 × 7) × 3 × 3 = (5 × 7 × 3) × (5 × 7 × 3) = (5 × 7 × 3)2 = (105)2 (ii) 2156 At first, We’ll resolve the given number into prime factors: Hence, 2156 = 4 × 11 × 49 = 7 × 7 × 2 × 2 × 11 = (2 × 7) × (2 × 7) × 11 In the above factors only 11 is unpaired So, in order to get a perfect square the given number should be multiplied by 11 Hence, The number whose perfect square is the new number is as following: = (2 × 7) × (2 × 7) × 11 × 11 = (2 × 7 × 11) × (2 × 7 × 11) = (5 × 7 × 11)2 = (154)2 (iii) 3332 At first, We’ll resolve the given number into prime factors: Hence, 3332 = 4 × 17 × 49 = 7 × 7 × 2 × 2 × 17 = (2 × 7) × (2 × 7) × 17 In the above factors only 17 is unpaired So, in order to get a perfect square the given number should be multiplied by 17 Hence, The number whose perfect square is the new number is as following: = (2 × 7) × (2 × 7) × 17 × 17 = (2 × 7 × 17) × (2 × 7 × 17) = (2 × 7 × 17)2 = (238)2 (iv) 2925 At first, We’ll resolve the given number into prime factors: Hence, 2925 = 9 × 25 × 13 = 3 × 3 × 13 × 5 × 5 = (5 × 3) × (5 × 3) × 13 In the above factors only 13 is unpaired So, in order to get a perfect square the given number should be multiplied by 13 Hence, The number whose perfect square is the new number is as following: = (5 × 3) × (5 × 3) × 13 × 13 = (5 × 3 × 13) × (5 × 3 × 13) = (5 × 3 × 13)2 = (195)2 |
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