Prove that 7√5 are irrational
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Sia ? 6 years, 4 months ago
We can prove {tex}7 \sqrt { 5 }{/tex} irrational by contradiction.
Let us suppose that {tex}7 \sqrt { 5 }{/tex} is rational.
It means we have some co-prime integers a and b (b≠ 0)
such that
{tex}7 \sqrt { 5 } = \frac { a } { b }{/tex}
{tex}\Rightarrow \sqrt { 5 } = \frac { a } { 7 b }{/tex} .......(1)
R.H.S of (1) is rational but we know that {tex}\sqrt { 5 }{/tex} is irrational.
It is not possible which means our supposition is wrong.
Therefore, {tex}7 \sqrt { 5 }{/tex} cannot be rational.
Hence, it is irrational.
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