Question

prove 5√6 is irrational​

Answer 1

On the contrary,let us assume 5√6 is a rational number

Now,

5√6=p/q

where p and are natural numbers and q≠0.

→√6=p/5q

Clearly,√6 is an irrational but the number on the RHS is a rational

But a rational can't be an irrational

So,LHS≠RHS

As this contradicts our assumption,5√6 is an irrational number

Hence,proved

Answer 2

Answer:

5√6 is a irrational number.

Proved!

Step-by-step explanation:

Given Problem:

Prove 5√6 is irrational​

To Prove:

5√6 is irrational​

Solution:

Let us assume,

5√6 is a rational number where 5√6 = $\dfrac{p}{q}$

Here,

★We are assuming the above statement because in mathematics few sums can only be done with the method of assumption.★

But,

q ≠ 0          

★Because q is in the denominator, if denominator is zero then we won’t get a proper solution.★

Therefore,

From our assumption,

We have to continue the remaining steps,

5√6= $\dfrac{p}{q}$

√6= $\dfrac{a}{5} b$

Hence √6 is an irrational number which is not equal to $\dfrac{a}{5} b$ and it’s a rational number

So,

Our assumption is wrong!

Therefore,

5√6 is a irrational number!

Hence,Proved!