Question

HCF of two numbers is 17. If the square root of product of the numbers is a three-
digit perfect square number, then the sum of the numbers is
off​

Answer 1

Given : HCF of two numbers is 17.  square root of product of the numbers is a three-  digit perfect square number

To Find : sum of the numbers

Solution:

HCF of two numbers is 17.

So Two numbers are

17a  & 17b

where a & b are co prime

square root of product of the numbers is a three-  digit perfect square number,

√17a*17b  =  17√ab  

17√ab   is perfect Square hence it can

17 x 17   = 289   as 17 is prime number

17 x 17 x 2² = 1156 >  3 Digits  

so only possible is √ab  = 17

√ab  = 17  

ab = 289

289 = 1 x 289

or 17 x 17

a & b are co prime hence

a & b are = 1  & 289  in any order

so numbers are

17   & 17 x 289

Sum of numbers

= 17 + 17(289)

= 17(1 + 289)

= 17(290)

= 4,930

sum of the numbers is  4,930

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