Maths problem
√5-3√2 is irrational number prove it
Please solve the answer help me
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Let √5 - 3√2 be a rational number.
•°•
√5 - 3√2 = a / b
√5 = ( a / b ) + 3√2
√5 = ( a + 3√2 ) / b
Squaring both sides, we get
( √5 )² = [ ( a + 3√2 ) / b ]²
5 = ( a + 3√2 )² / b²
On right - Hand side, if we solve, the answer come will be an irrational number. But on left hand side, 5 is a rational number.
Hence, our contradiction was wrong.
Therefore, √5 - 3√2 is an irrational number.
•°•
√5 - 3√2 = a / b
√5 = ( a / b ) + 3√2
√5 = ( a + 3√2 ) / b
Squaring both sides, we get
( √5 )² = [ ( a + 3√2 ) / b ]²
5 = ( a + 3√2 )² / b²
On right - Hand side, if we solve, the answer come will be an irrational number. But on left hand side, 5 is a rational number.
Hence, our contradiction was wrong.
Therefore, √5 - 3√2 is an irrational number.
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