Question

show that 5 root 6 is an irrational number

Answer 1

Answer:

5√6 is irrational.

Step-by-step explanation:

$Let \: us \: assume , \: \\the \: contrary ,\:that \: 5\sqrt{6}\\ \: is \: rational .$

$i.e., we \: can \: find \\\: co-primes \:a \: and \: b \: (b≠0)\: \\such \: that \:5\sqrt{6}=\frac{a}{b}.$

$We \: get \sqrt{6}=\frac{a}{5b}.$

Since , 5, a and b are integers ,

$\frac{a}{5b} \: is \: rational$,and so √6 is rational.

But this contradicts the fact that √6 is irrational.

So, we conclude that 5√6 is irrational.

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Answer 2

Answer:

Let us assume 5√6 is a rational number where 5√6 =a/b

[Here we are assuming the above statement because in mathematics few sums can only be done with the method of assumption]

But b ≠ 0           [Because b is in the denominator, if denominator is zero then we won’t get a proper solution]

Therefore from our assumption we continue the remaining steps

5√6=a/b

√6=a/5b

Hence √6 is an irrational number which is not equal to a/5b and it’s a rational number

So our assumption is wrong ,

Therefore 5√6 is a irrational number