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Prove that Root3 is irrational number

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Prove that Root3 is irrational number

Posted by Aakash Anand 4 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Aakash Anand 4 years, 6 months ago

If possible let √3 is a rational number Let √3 =a/b {a and b is co- prime number} = b√3 =a [ squaring both side] [ b√3]²=[a]² = 3b²=a²................. (1) 3 is divides a² Their for 3 divides a Let a= 3c [ c is positive integer] Putting a=3c in equation (1) # 3b²= (3c) ² # 3b² = 9c² # b²= 3c² 3 is divides b² Their for 3 divides b 3 is common factor of A and B But It contradict the fact a and b are co-prime number So our assumlat is wrong Their for √ 3 is an irrational number. .......... Aakash Anand ?

4Thank You

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