i. \(\sqrt[3]{51}\) is a surd because 51 is a positive rational number, 3 is a positive integer greater than 1 and \(\sqrt[3]{51}\) is irrational.
ii. \(\sqrt[4]{16}\) is not a surd because
= 2, which is not an irrational number.
iii. \(\sqrt[5]{81}\) is a surd because 81 is a positive rational number, 5 is a positive integer greater than 1 and \(\sqrt[5]{81}\) is irrational.
iv. \(\sqrt{256}\) is not a surd because
= 16, which is not an irrational number.
v. \(\sqrt[3]{64}\) is not a surd because
= 4, which is not an irrational number.
vi. \(\sqrt{22/7}\) is a surd because 22/7 is a positive rational number, 2 is a positive integer greater than 1 and \(\sqrt{22/7}\) is irrational.