all surds are irrational but irrational are not surds
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By definition, a surd is a irrational root of a rational number. So we know that surds are always irrational and they are always roots.
For eg, √2 is a surd since 2 is rational and √2 is irrational.
Similarly, cube root of 9 is also a surd since 9 is rational and cube root of 9 is irrational.
On the other hand, √π is not a surd even though √π is irrational, because π is not rational.
Thus, to answer the question, every surd is a irrational number, though an irrational number may or may not be a surd.
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