Question

$show \: that \: 5 \sqrt{6} \: is \: irrtional \: number$


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Answer 1

$\huge\underline\mathrm{Question}:-$

Show that 5√6 is irrational number.

$\huge\underline\mathrm{Solution}:-$

Let 5√6 be a rational number, which can be expressed as a/b, where b≠0 and a and b are the integers

⇒ 5√6 = a/b

⇒ √6 = a/5b

⇒ √6 = rational

But √6 is an irrational number.

Thus, assumption is wrong.

Hence, 5√6 is irrational number.