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2-√3 is an irrational no. Prove …

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2-√3 is an irrational no. Prove that

Posted by Ritesh Tanwer 6 years, 11 months ago

CBSE > Class 10 > Mathematics

2 answers

Lionel Messi⚽️ 6 years, 11 months ago

Please 5 ki jagah 2 rakhna . Baki sabh teekh hai.

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Lionel Messi⚽️ 6 years, 11 months ago

• Let us assume , to the contrary , that 2 - root 3 is rational. •That is ,we can find coprime a and b (b= not epuals to 0) such that 2- root 3= a/b. • Therefore , 2- a/b= root 3. • Rearranging this equation, we get root 3 = 5-a/b= 5b-a/b. • Since a and b are integers, we get 5-a/b is irrational, and so root 3 is rational. •But this contradicts the fact that root 3 is irrational. • This contradiction has arisen because of our incorrect assumption that 5-root 3 is rational. • So , we concluded that 5-root 3 is irrational. ● HENCE PROVED

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