prove that 3 + 2 root 2 is 1rrational
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let 3+2√2 be rational
so 3+2√2= a/b(where a and b are coprime nos and b is not equal to zero)
2√2=a/b-3
2√2=(a-3b)/3b
√2=(a-3b)/6b
Now,
(a-3b)/6b is rational since a/b is rational
but √2 is irrational.
therefore our assumption is wrong.
thus 3+2√2 is irrational
so 3+2√2= a/b(where a and b are coprime nos and b is not equal to zero)
2√2=a/b-3
2√2=(a-3b)/3b
√2=(a-3b)/6b
Now,
(a-3b)/6b is rational since a/b is rational
but √2 is irrational.
therefore our assumption is wrong.
thus 3+2√2 is irrational
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