Written as products of prime factors, \(240=2^4\times3\times5\) and \(2750=2\times5^3\times11\).
Find the smallest positive integer \(n\) for which \(\sqrt{2750n}\) is a whole number.[2]
Find the smallest positive integer \(k\) for which \(240k\) is a multiple of 2750.[1]
\(Y=a^{18}\times b^{12}\times c^{36}\), where \(a\), \(b\) and \(c\) are prime numbers. Explain why \(Y\) is a perfect cube.[1]