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Answers
Answer:
B) rational except when y = π.
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Answer:
Complete step-by-step answer:
An irrational number is a real number that cannot be represented as a ratio or a simple fraction.
Or an irrational number cannot be represented in the form pq,q≠0.
By definition, a surd is an irrational root of a rational number. So we know that surds are always irrational and they are always roots.
For example:
2–√ is a surd since 2 is a rational number as 2 is written as (21) and 2–√ is irrational number as 2–√ cannot represented in the form pq,q≠0.
Similarly, the cube root of 9 is also a surd since 9 is rational and the cube root of 9 is irrational.
⇒9–√3 Is an irrational number and 9 is a rational number.
On the other hand, π−−√ is not a surd because π is not a rational number it is an irrational number as π cannot be represented in the formpq,q≠0.
Thus, to answer the question, every surd is an irrational number.
But every irrational number may or may not be a surd for example π−−√
We know that every prime number is integer so it can’t be irrational. So option (B) is already rejected.
So this is the required answer.
Hence option (D) is correct.