Q1 of 54 Page 16

Prove that the following are irrational.

Let us suppose that is rational.

Let be rational equal to , where a and b are integers and a≠0 and b≠0 Then,



⇒


⇒ [squaring both sides]


⇒


⇒


⇒


⇒


Since a and b are integers, is rational. So, √3 is rational


Now, this contradicts the fact that √3 is rational.


Hence √3 + √5 is irrational.


More from this chapter

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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.

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Prove that the following are irrational.

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Prove that the following are irrational.

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Prove that the following are irrational.