Question

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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Answer 1

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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