Question

prove that √2-√5 is irrational​

Answer 1

Step-by-step explanation:

let us suppose√2-√5 is rational

then √2-√5=a/b

S.Q.B.S

2+5-2√10=a²/b²

7-2√10=a²/b²

-2√10=a²/b²-7

multiply with negative sign

2√10=7-a²/b²

√10=½(7-a²/b²)

Since irrational cannot be equal to rational

Hence our assumption that √2-√5 is rational

Hence,√2-√5 is irrational

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