Question

-Show that
5root6 is an irrational number​

Answer 1

To   prove5√6 is irrational.

Proof : This can be proved by the method of contradiction. Let's assume the given number to be rational.

∴ 5√6 = a/b [ where a and b are co primes]

⇒ √6 = a/5b

since, a , b and 5 are rational numbers so a/5b is  also rational. But this contradicts the fact that √6 is irrational number. This contradiction have a rising due to our wrong assumption that 5√6 is rational. Therefore, the given number is irrational number·

Answer 2

♡⚘✮ʜᴇʏᴀ ᴍᴀᴛᴇ ʜᴇƦᴇ ɪS ʏᴏᴜƦ ᴀɴSᴡᴇƦ :

$let \\ \: 5 \sqrt{6} be \: a \: rational \: number \\ \: which \: can \: be \: expressed \: as \: \frac{a}{b} \: \\ where \: b \: ≠0 \: and \: a \: b \: are \: integers \: \\ \\ = 5 \sqrt{6} = \frac{a}{b} \\ \sqrt{6} = \frac{a}{5b} \\ \sqrt{6} = rational \\ \: \\ but \: \sqrt{6} is \: is \: irrational \: \\ thus \: the \: assumption \: is \: wrong \: \\ hence \: 5 \sqrt{6} \: is \: a \: irrational \: number \: .$

♡ Hope it helps uh Plz maƦk as bƦainliest ♡