Question

find the smallest number by which the following number should be divided should as to perfect square also find the square root of the number as obtained 102487​

Answer 1

Answer:

)                 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. (i) 252                                    (ii) 2925                (iii) 396                                  (iv) 2645 (v) 2800                                (vi) 1620

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Answer:

                (i) 252 The prime factorisation of 252 is 

252=2×2×3×3×7

. We see that the prime factor 7 has no pair. So, if we divide 252 by 7, then we get  225221263633217

252÷7=2×2−−−−×3×3−−−−

. Now each prime factor has a pair. Therefore, 252 - 7 = 36 is a perfect square. Thus, the required smallest number is 7. Hence, 

36−−√=2×3=6

. (ii) 2925 The prime factorisation of 2925 is

2925=3×3×5×5×13

. We see that the prime factor 13 has no pair. So, if we divide 2925 by 13, then we get329253975532556513  

2925÷13=3×3−−−−=5×5−−−−

Now each prime factor has a pair. Therefore, 

2925÷13=225

 is a perfect square. Thus, the required smallest number is 13. Hence, 

225−−−√=3×5=15

. (iii) 396 The prime factorisation of 396 is

396=2×2×3×3×11

 . We see that the prime factor 11 has no pair. So if we divide 396 by 11, then we get  2396219839933311

396÷11=2×2−−−−×3×3−−−−

 Now each prime factor has a pair. Therefore, 

396÷11=

Answer 2

Step-by-step explanation:

factors of 102487

7x11^3 so as to be a square multiply by 11x7

(7x11^2)^2

7x121=

847

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