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Q.

Choose whether the given statement is true or false.

Every surd is irrational, but every irrational need not be a surd.

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a

True

b

False

answer is A.

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Detailed Solution

By definition, a surd is an irrational root of a rational number. So now we know that surds are always irrational and they are always roots.
For example, square root of 2 i.e. 2 is a surd since 2 is rational and square root of

\sqrt{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 and e are not surds even though they are irrational, because they are not the roots of any algebraic expression.
So, the given statement is true.
Hence (1) is the correct option.

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