Question

21. Show that 5V6 is an irrational number.​

Answer 1

Answer:

Step-by-step explanation:

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.

Answer 2

Step-by-step explanation:

                                                                                                            a

Let us assume, to the contrary, that 5$\sqrt 6$ rational. Then, 5$\sqrt 6$ =  b

 where (b≠0) and a & b are co-prime positive integers.

Then,

             5$\sqrt6$ = a

                         b      

                $\sqrt6$ =  a  

                          5b

 Since 3,a,b are integers ,  a     is rational.

                                               5b

So, $\sqrt{6$ is also rational                         (     $\sqrt6$ =  a      )

                                                                                5b

               

But this contradicts the fact that $\sqrt6$  is irrational.

This contradiction has arisen because of our incorrect assumption that

5$\sqrt6$   is rational.

Hence, our assumption is wrong, 5$\sqrt6$ is irrational.

               Hence proved.