prove that 5-2√3 is irrational
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HI!!!
Assume that 5-2 root 3 is rational
5-2 root 3 = a/b, where a and b are integers.
-2 root 3 = a/b -5
2 root 3 = 5 - a/b
2 root 3 = 5b/b - a/b
root 3 = 5b - a / 2b
We know that a, b,2 and 5 are integersand they are also rational
therefore root 3 will be rational
but we know that root 3 is irrational
there is a contradiction.
So 5-2 root 3 is irrational number.
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Assume that 5-2 root 3 is rational
5-2 root 3 = a/b, where a and b are integers.
-2 root 3 = a/b -5
2 root 3 = 5 - a/b
2 root 3 = 5b/b - a/b
root 3 = 5b - a / 2b
We know that a, b,2 and 5 are integersand they are also rational
therefore root 3 will be rational
but we know that root 3 is irrational
there is a contradiction.
So 5-2 root 3 is irrational number.
Hope it is useful ^ _ ^ Pls mark me as brainliest
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