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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) Given 3675 Resolve 3675 into prime factors, we get 3675 = 3 X 5 X 5 X 7 X 7 Now to get perfect square we have to multiply the above equation by 3 Then we get, 3675 = 3 X 3 X 5 X 5 X 7 X 7 = (3 X 52 X 72) New number = (9 X 25 X 49) = (32 X 52 X 72) Taking squares as common from the above equation we get ∴ New number = (3 X 5 X 7)2 = (105)2 Hence, the new number is square of 105 (ii) Given 2156 Resolve 2156 into prime factors, we get 2156 = 2 X 2 X 7 X 7 X 11 = (22 X 72 X 11) Now to get perfect square we have to multiply the above equation by 11 Then we get, 2156 = 2 X 2 X 7 X 7 X 11 X 11 New number = (4 X 49 X 121) = (22 X 72 X 112) Taking squares as common from the above equation we get ∴ New number = (2 X 7 X 11)2 = (154)2 Hence, the new number is square of 154 (iii) Given 3332 Resolve 3332 into prime factors, we get 3332 = 2 X 2 X 7 X 7 X 17= (22 X 72 X 17) Now to get perfect square we have to multiply the above equation by 17 Then we get, 3332 = 2 X 2 X 7 X 7 X 17 X 17 New number = (4 X 49 X 289) = (22 X 72 X 172) Taking squares as common from the above equation we get ∴ New number = (2 X 7 X 17)2 = (238)2 Hence, the new number is square of 238 (iv) Given 2925 Resolve 2925 into prime factors, we get 2925 = 3 X 3 X 5 X 5 X 13= (32 X 52 X 13)Now to get perfect square we have to multiply the above equation by 13 Then we get, 2156 = 3 X 3 X 5 X 5 X 13 X 13 New number = (9 X 25 X 169) = (32 X 52 X 132) Taking squares as common from the above equation we get ∴ New number = (3 X 5 X 13)2 = (195)2 Hence, the new number is square of 195 |
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