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Solution: We have to find the smallest whole number by which the number should be divided so as to get a perfect square number To get a perfect square, each factor of the given number must be paired. (i) 252  Hence, prime factor 7 does not have its pair. If the number is divided by 7, then the rest of the prime factor will be in pairs. Therefore, 252 has to be divided by 7 to get a perfect square. 252 ÷ 7 = 36 36 is perfect square 36 = 2 × 2 × 3 × 3 = 22 × 32 = (2 × 3)2 Thus, √36 = 2 × 3 = 6 (ii) 2925 Hence, prime factor 13 does not have its pair. If the number is divided by 13, then the rest of the prime factor will be in pairs. Therefore, 2925 has to be divided by 13 to get a perfect square. 2925 ÷ 13 = 225 225 is a perfect square 225 = 5 × 5 × 3 × 3 = 52 × 32 = (5 × 3)2 Thus, √225 = 15 (iii) 396 Hence, prime factor 11 does not have its pair. If the number is divided by 11, then the rest of the prime factor will be in pairs. Therefore, 396 has to be divided by 11 to get a perfect square. 396 ÷ 11 = 36 36 is a perfect square 36 = 3 × 3 × 2 × 2 = 32 × 22 = (3 × 2)2 Thus, √36 = 3 × 2 = 6 (iv) 2645 Hence, prime factor 5 does not have its pair. If the number is divided by 5, then the rest of the prime factor will be in pairs. Therefore, 2645 has to be divided by 5 to get a perfect square. 2645 ÷ 5 = 529 529 is a perfect square 529 = 23 × 23 = 232 Thus, √529 = 23 (v) 2800 Hence, prime factor 7 does not have its pair. If the number is divided by 7, then the rest of the prime factor will be in pairs. Therefore, 2800 has to be divided by 7 to get a perfect square 2800 ÷ 7 = 400 400 is a perfect square 400 = 2 × 2 × 2 × 2 × 5 × 5 = 22 × 22 × 52 = (2 × 3 × 5)2 Thus, √400 = 2 × 2 × 5 = 20 (vi) 1620 Hence, prime factor 5 does not have its pair. If the number is divided by 5, then the rest of the prime factor will be in pairs. Therefore, 1620 has to be divided by 5 to get a perfect square. 1620 ÷ 5 = 324 324 is a perfect square 324 = 2 × 2 × 3 × 3 × 3 × 3 = 22 × 32 × 32 = (2 × 3 × 3)2 Thus, √324 = 2 × 3 × 3 = 18 ☛ Check: NCERT Solutions for Class 8 Maths Chapter 6 Video Solution: 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. |
What is the smallest whole number which must be added to 2800 in order to get a perfect square number?
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