Q1 of 54 Page 16

Prove that the following are irrational.

Let be rational. Then, there exists positive co-primes a and b such that



⇒


⇒


⇒


is rational as a and b are integers


∴√2 is rational which contradicts to the fact that √2 is irrational.


Hence, our assumption is false and is irrational.


More from this chapter

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3

Write the following rationales in decimal form using Theorem 1.1.

(i)


(ii)


(iii)


(iv)


(v)

4

The decimal form of some real numbers is given below. In each case, decide whether the number is rational or not. If it is rational, and expressed in form what can you say about the prime factors of q?

(i) 43.123456789


(ii) 0.120120012000120000….


(iii) 43.

 1

Prove that the following are irrational.

 1

Prove that the following are irrational.