CBSE Maths for Class 10th Irrational Numbers from Real Numbers Irrational Numbers Theorem 4 Prove that √ 11 is irrational. Proof:-let √ 11 be rational and let its simplest form a/b. Then a and b are integers having no common factor other than 1 and b is not equal 0 √11=a/b 11=a²/b² on squaring both sides 11b²=a² 11 divide a² 11 divide b² 11 divide a 11 is prime and 11 divides a² Let a =11c for some positive integer c Putting a =11c in, we get 11b²=121c² b²=11c² 11 divide b² 11 divide b Thus 11 is a common factor of a and b. Know more ...
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