Question

what is the smallest number by which 17496 must be multiplied so that the product is a perfect cube

Answer 1

let the smallest no be x
atq
by primefactorisation 17496
by prime factorisation 2*2*2*3/3*3*3*3*3*3 now group them into pair of 3 we see that 3 is left so it must be multiplied by 3*3 = 9

Answer 2

Step-by-step explanation:

17496=3*5832=3*3*1944=3*3*3*648=3*3*3*3*216=3*3*3*3*3*72=3*3*3*3*3*3*24=3*3*3*3*3*3*2*2*2*3 so the smallest number is 3 by which 17496 must be divided to get 5832 whose cube root is 3*3*2=18.