Irrational numbers and proofs of irrationalityPractice Questions & MCQs
Practice Irrational numbers and proofs of irrationality questions from Real Numbers (Class 10 Maths) - important MCQs with answers and step-by-step solutions. Solve the sample questions below, then practice the full set free on the RankByte app.
Irrational numbers and proofs of irrationalityQuiz - Solve & Score
Q1. A baker at a flour mill wraps a string once around a circular rim and notes the value pi times the diameter. How should this number be classified?
- A.a prime number
- B.an integer
- C.irrational
- D.rational
Answer: C. irrational
A number is rational if it is p/q with integers p,q (q!=0), i.e. terminating or repeating; otherwise irrational. Here pi is non-terminating non-repeating, so the number is irrational.
Q2. An electrician at a survey camp finds the slant of a 1-by-2 rectangle to be sqrt(5) units. How should this number be classified?
- A.rational
- B.irrational
- C.an integer
- D.a prime number
Answer: B. irrational
A number is rational if it is p/q with integers p,q (q!=0), i.e. terminating or repeating; otherwise irrational. Here sqrt(5) is the root of a non-perfect square, so the number is irrational.
Q3. A jeweller in a foundry computes the side of a 49 square-centimetre tile as sqrt(49). How should this number be classified?
- A.rational
- B.an integer
- C.a prime number
- D.irrational
Answer: A. rational
A number is rational if it is p/q with integers p,q (q!=0), i.e. terminating or repeating; otherwise irrational. Here sqrt(49)=7, an integer, so the number is rational.
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Yes. These Irrational numbers and proofs of irrationality important questions follow the Maths exam pattern (CBSE Boards, plus JEE and NEET foundation), so they help with both school and competitive prep.
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