Question

prove that root5 - root 2 is an irrational number​

Answer 1

Answer:

Step-by-step explanation:

et root 5-root2 be a rational number that is it can be expressed in the form of p/q where both p and q are integer and q is not equal to 0.

after solving our contradiction becomes wrong and hence we can say that the number is an irrational number

Answer 2

Answer:

To Prove:-

√5+√2 is an irrational number

Proof:-

Let us assume through the contradictory that √5-√2 is a rational number . Then there exist co-prime positive integers a and b

√5+√2 =a/b

√5= a/b - √2

(√5)2 = (a/b - √2)2 (Squaring both side)

5 = a2/b2 + 2 - 2a√2/b

a2/b2 -3 = 2a√2/b

a2 -3b2/2ab =√2

√2 is a rational number

This contradicts that √2 is irrational

So our assumption is wrong

√5+√2 is a irrational number

your question is somewhat incorrect it becomes very complex so in place of √5-√2 it is √5+√2

hope this will help you!!