Question

show that root 5 - 2 root 7 is an irrational number​

Answer 1

Answer:

let us assume that√5-2√7 is rational.

√5-2√7= a/b (where a and b are co-primes,ais not equal to 0)

now let's do squaring on both sides

(√5-2√7 )² = (a/b)²

(√5)² -2*√5*2√7+(2√7)²= a²/b²

5 -4√35 +(4*7)= a²/b²

5-4√35+28=a²/b²

33-4√35=a²/b²

-4√35=a²/b²-33

-4√35=a²-33b²/b²

so

-4√35 is irrational whereas a²-33b²/b² is rational

So our assumption is wrong to state that √5-2√7 is rational

Answer 2

Answer:

arey

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