Compare the Surds 6 √2 , 5√5
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√2 (square root of 2) can’t be simplified further so it is a surd
√4 (square root of 4) CAN be simplified to 2, so it is NOT a surd
Comparison of Surds
In the comparison of surds, we will discuss the comparison of equiradial surds and comparison of non-equiradical surds.
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In comparison of surds we will discuss about the comparison of equiradical surds and comparison of non-equiradical surds.
I. Comparison of equiradical surds:
In case of equiradical surds (i.e., surds of the same order) n
√
a
and n
√
b
, we have n
√
a
> n
√
b
when x > y.
For example,
(i) √5 > √3, since 5 > 3
(ii) ∛21 < ∛28, since 21 < 28.
(iii) ∜10 > ∜6, since 10 > 6.
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