show that 3+2√5 is an irrational number
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Hello!!
3 + 2√5 = a/ b
2√5 =a/b -3
√5 =a-3b/2b
√5 is rational.
This contradicta the fact that √5 is irrational.
So our supposition is incorrect.
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Hey mate this may
useful to you
Let us assume to the contrary that 3+2√5 is rational
That is, we can find coprimes 'a' and 'b' (b not equal to 0) such that
3+2√5=a/b
2√5=a/b -3 is rational
a and b are integers
therefore, a/b -3 is rational.
√5= a/b-3 /2 is also rational.
This contradiction has arisen because of our assumptions that 3+2√5 is rational.
therefore, 3+2√5 I'd irrational .
useful to you
Let us assume to the contrary that 3+2√5 is rational
That is, we can find coprimes 'a' and 'b' (b not equal to 0) such that
3+2√5=a/b
2√5=a/b -3 is rational
a and b are integers
therefore, a/b -3 is rational.
√5= a/b-3 /2 is also rational.
This contradiction has arisen because of our assumptions that 3+2√5 is rational.
therefore, 3+2√5 I'd irrational .
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