It is an irrational number that lies between 7 and 8
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Only two prime numbers lie between 50 and 60. They are 53 and 59.
Let's call this number b 42000 = 24 x 3 x 53 x 7 We have 42000 x b = a2 and a is an integer Then a = sqrt(42000 x b) = sqrt(b) x sqrt(24 x 3 x 53 x 7) sqrt(24 x 3 x 53 x 7) = 22 x sqrt(3) x 5 x sqrt(5) x sqrt(7) For a to be an integer sqrt(b) must be sqrt(3) x sqrt(5) x sqrt(7) at least Thus b = 105
Counting only integer square roots, since sqrt(5) is equal to ±25 and sqrt(6) is equal to ±36, the square roots of the integers between 25 and 36, and between -36 and -25, are between 5 and 6 inclusive.
-sqrt(59) < -3, 6 < sqrt(59)
sqrt(6*10) = sqrt(60) = 7.75 (approx)