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CBSE Maths for Class 10th Irrational Numbers from Real Numbers

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.
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