Classify the given pair of surds into like surds and unlike surds.i.√ 52,5√ 13 ii.√ 68.5√ 3,iii.4√ 18,7√ 2

Question

Classify the given pair of surds into like surds and unlike surds.

i. \(\sqrt{52} \), \(5\sqrt{13}\)

ii.\(\sqrt{68} \), \(5\sqrt{3}\)

iii.\(4\sqrt{18}\), \(7\sqrt{2}\)

iv. \(19\sqrt{12}\), \(6\sqrt{3}\)

v. \(5\sqrt{22}\), \(7\sqrt{33}\)

vi. \(5\sqrt{5}\), \(\sqrt{75}\)

Answer 1

i. If the order of the surds and the radicands are same, then the surds are like surds.

Here, the order of 2\(\sqrt{13}\) and 5 is same 5\(\sqrt{13}\) and their radicands are also same.

∴ \(\sqrt{52}\) and 5\(\sqrt{13}\) are like surds.

Here, the order of 2\(\sqrt{17}\) and 5 \(\sqrt{5}\) is same but their radicands are not. 

∴ \(\sqrt{68}\) and 5\(\sqrt{3}\) are unlike surds.

Here, the order of 12\(\sqrt{2}\) and 7\(\sqrt{2}\) is same and their radicands are also same.

∴ 4\(\sqrt{18}\) and 7\(\sqrt{2}\) are like surds.

Here, the order of 38\(\sqrt{3}\) and 6\(\sqrt{3}\) is same and their radicands are also same.

∴ 19\(\sqrt{12}\) and 6\(\sqrt{3}\) are like surds.

v. \(5\sqrt{22}\),\(7\sqrt{33}\)

Here, the order of \(5\sqrt{22}\) and \(7\sqrt{33}\) is same but their radicands are not. 

∴ \(5\sqrt{22}\) and \(7\sqrt{33}\) are unlike surds.

Here, the order of \(5\sqrt{5}\) and \(5\sqrt{3}\) is same but their radicands are not. 

∴ \(5\sqrt{5}\) and \(5\sqrt{3}\) are unlike surds.