Show that 5 is an irrational numbers. [Use division method] - Vidyadip

Question

Show that $\sqrt{5}$ is an irrational numbers. $[$Use division method$]$

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Answer

$2.23606...$
$2$	$5.0000000000... -4$
$42$	$100 -84$
$443$	$1600 -1329$
$4466$	$27100 -26796$
$447206$	$3040000 -2683236$
$ $	$356764 ...$

Clearly, $\sqrt{5}=2.23606 \ldots . . . ;$
which is an irrational number.
Hence, $\sqrt{5}$ is an irrational number.

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