Question

Given that √5 is irrational. Prove that 6 - √5is irrational.​

Answer 1

Answer:

prove 6+√5is a irrational nos

Let us assume, to the contrary, that 6+√5 is irrational.

So we can find two integers numbers p and q(≠0), in the following way,

6+√5 = p/q [where p and q are co-prime]

Rearranging,

√5 = p/q - √6

√5 = [p - √6q]/q

But [p - √6q]/q is a rational nos

By fact √5 is a rational nos

our assumption is wrong

6+√5 is irrational nos

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