Question

1. Classify the following numbers as rational or irrational:

(i) 2 - √5 (ii) (3 +√ 23) - √23 (iii)
2√7/7√7​

Answer 1

Answer:

(i)irrational

(ii)rational

(iii)rational

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Answer 2

Answer:

√7 is not a perfect square root, so it is an irrational number. We have, ∴√4 can be expressed in the form of , p/ q, so it is a rational number. The decimal representation of √4 is 2.0. 2 is a rational number, whereas √3 is an irrational number. Because, sum of a rational number and an irrational number is an irrational number, so 2 +√3 is an irrational number. √ 2 is an irrational number. Also √3 is an irrational number. The sum of two irrational numbers is irrational. √ 3+√ 2 is an irrational number. √ 5 is an irrational number. Also √3 is an irrational number. The sum of two irrational numbers is irrational. √ 3 +√5 is an irrational number. We have, Now, 6 is a rational number, whereas 4√2 is an irrational number. The difference of a rational number and an irrational number is an irrational number. So, 6- 4√2 is an irrational number. (√2 - 2 ) 2 is an irrational number. We have, Since 2 is a rational number. (2 -√2 )(2 +√2) is a rational number. We have, The sum of a rational number and an irrational number is an irrational number, so 5+2√6 is an irrational number.