Q . n is a natural number divisible by 75. If n^2is written in decimal notation as 5k05h25, then find the value of k^2 + 4h.
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Answers
Given : n is a natural number divisible by 75 . n² is written in decimal notation as 5k05h25,
To find : Value of k² + 4h
Solution:
n is a natural number divisible by 75.
=> n = 75a
n² = (75a)²
=> n² = 5625a²
n² = 5k05h25
=> minimum n² = 5005025
=> n² ≥ 5005025
=> n ≥ 2,238
n = 75 a
=> 75 a ≥ 2,238
=> a ≥ 30
Lets try a = 30
75 * 30 = 2250 & 2250² = 50,62,500 Does not match with 5k05h25
now lets try a = 31
=> 75 * 31 = 2325 & 2325² = 54,05,625 match with 5k05h25
Hence k = 4 & h = 6
k² + 4h = 4² + 4(6) = 16 + 24 = 40
value of k² + 4h = 40
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