prove that 4_5root2 is irrational
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Let us assume that 4-5√2 is rational.
4 - 5√2 = a/b
=> -5√2 = a/b - 4
=> 5√2 = 4 - a/b
=> 5√2 = (4b - a)/b => √2 = (4b - a)/5b
As we know that √2 is irrational and
{(4b - a)/5b } is rational which is not equal to each other. But according to our assumption √2 is rational which is a contradiction.
Therefore, 4-5√2 is irrational.
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4 - 5√2 = a/b
=> -5√2 = a/b - 4
=> 5√2 = 4 - a/b
=> 5√2 = (4b - a)/b => √2 = (4b - a)/5b
As we know that √2 is irrational and
{(4b - a)/5b } is rational which is not equal to each other. But according to our assumption √2 is rational which is a contradiction.
Therefore, 4-5√2 is irrational.
hope it helps you, pls Mark the brainliest
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