prove that 3+√5is an irrational number
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Answer:
Given 3 + √5
To prove:3 + √5 is an irrational number.
Proof:
Letus assume that 3 + √5 is a rational number.
So it can be written in the form a/b
3 + √5 = a/b
Here a and b are coprime numbers and b ≠ 0
Solving
3 + √5 = a/b
we get,
=>√5 = a/b – 3
=>√5 = (a-3b)/b
=>√5 = (a-3b)/b
This shows (a-3b)/b is a rational number.
But we know that √5 is an irrational number, it is contradictsour to our assumption.
Our assumption 3 + √5 is a rational number is incorrect.
3 + √5 is an irrational number
Hence proved.
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