Question

Show that 7-√5 is irrational give that √5 is irrational

Answer 1

Here is your answer mate ☺️☺️✌️✌️✅✅

Let ,

7-√5 is a rational no. is equals to r, where r is a rational no.

So,

7-√ 5 = r

7-r = √5.

Now,

LHS is a rational but RHS is an irrational.

So, our assumption was wrong; 7-√5 is not a rational no.

Therefore, 7-√5 is a irrational no.

Hence, proved.

Hope this will help you...☺☺

Answer 2

Answer:

Here is your answer!

Step-by-step explanation:

Let us assume that 7-√5 is irrational,

Then, 7-√5 = p/q ( where p and q are coprime integers)

Rearranging,

7- p/q = √5

7q - p/q = √5

Since q and p are integers, 7q - p/q is rational.

But we know that √5 is irrational

This contradiction has arisen due to our incorrect assumption,

Therefore, 7- √5 is irrational.

Hope that it helped!