Question

Prove that √6 + √5 is irrational.

Answer 1

Answer:- 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 number

By fact √5 is a rational number

our assumption is wrong

6+√5 is irrational number.

Hope it helps!

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