Question

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

iv. 19√12, 6√3

v. 5√22, 7√33

vi. 5√5, √75

Answer 1

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

i. 

Here, the order of 2√13 and 5√13 is same and their radicands are also same. 

∴ √52 and 5√13 are like surds.

ii. 

Here, the order of 2√17 and 5√3 is same but their radicands are not. 

∴ √68 and 5√3 are unlike surds.

iii. 

Here, the order of 12√2 and 7√2 is same and their radicands are also same. 

∴ 4√18 and 7√2 are like surds.

iv. 

Here, the order of 38√3 and 6√3  is same and their radicands are also same. 

∴ 19√12 and 6√3 are like surds.

v. 5√22, 7√33

Here, the order of 5√22 and 7√33 is same but their radicands are not. 

∴ 5√22 and 7√33 are unlike surds.

vi. 

Here, the order of 5√5 and 5√3 is same but their radicands are not. 

∴ 5√5 and √75 are unlike surds.