The smallest number, which multiplies to $33275$ to get a perfect cube, is

1. Find the prime factorization of $33275$:
$$33275÷5=6655$$
$$6655÷5=1331$$
$$1331÷11=121$$
$$121÷11=11$$
$$11÷11=1$$
$$33275=5^2\times 11^3$$
For a number to be a perfect cube, the exponents of all its prime factors must be multiples of 3.In the factorization $5^2\times 11^3$, the prime factor 11 forms a perfect triplet ($11^3$), but the prime factor 5 only has a power of 2 ($5^2$). To form a triplet ($5^3$), we need to multiply by one more 5.Therefore, the smallest number required is 5.