Q. 34.1( 27 Votes )

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 :

Two or more surds are said to be similar or like surds if they have the same surd-factor.


And,


Two or more surds are said to be dissimilar or unlike when they are not similar.


Therefore,


i. √52, 5√13


√52 = √(2×2×13) = 2√13


5√13


both surds have same surd-factor i.e., √13.


they are like surds.


ii. √68, 5√3


√68 = √(2×2×17) = 2√17


5√3


both surds have different surd-factors √17 and √3.


they are unlike surds.


iii. 4√18, 7√2


4√18 = 4√(2×3×3) = 4×3√2 = 12√2


7√2


both surds have same surd-factor i.e., √2.


they are like surds.


iv. 19√12, 6√3


19√12 = 19√(2×2×3) = 19×2√3 = 38√3


6√3


both surds have same surd-factor i.e., √3.


they are like surds.


v. 5√22, 7√33


both surds have different surd-factors √22 and √33.


they are unlike surds.


vi. 5√5, √75


5√5


√75 = √(5×5×3) = 5√3


both surds have different surd-factors √5 and √3.


they are unlike surds.


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