Question

Hence, find the smallest possible value of k, for which 360k is;

a) a perfect square, ( /2) b) a perfect cube. ( /2)
please help its urgent i am having a test

Answer 1

$\huge\red{answer}$⇒here we have to find with how many perfect square numbers i.e. 4,9,16,25,... it is divisible.

any number whose sum of digits is divible by 9 must itself be divisible by 9.

if we add the digits of the number we get 1+5+7+5=18 which is a multiple of 9 so it must be divisible by 9.

dividing with 9 we get

(1575 x k)/9 = 175 x k

any figure which ends in 25, or 50, or 75 or 00 must be divisible by 25

further dividing with 25 we get = 7 x k

therefore k must be equal to 7 to make it a perfect square.

hence 7 is the smallest number to make it a perfect square.

$\huge\orange{@alurringbabe}$