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Prove that underroot3 is a irrational …

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Prove that underroot3 is a irrational no

Posted by Naina Chauhan 7 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Maitreyee Dave 7 years, 4 months ago

Let √3 be rational no. Then it exist in the form p/q where q≠0 √3=p/q. (here slash means upon) (on squaring both side) (√3)²= (p/q)² 3=p²/q² q²=p²/3. -------(1) From (1) we noticed that p² is divisible by 3 therefore p is also divisible by 3 -----(2) Now put p=3r in (1) Therefore q²= (3r)²/3 So, q²= 9r²/3 q²= 3r² (÷3) q²/3= r² OR r²= q²/3-----(3) From (3) we noticed that q² is divisible by 3 therefore q is also divisible by 3 ------(4) So by (2) & (4) it contradicts our suppose that √3 is rational but it is irrational because both p and q are divisible by 3 Hence proved

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