Question

Prove that√7+√5 is an irrational numbers

Answer 1

Answer:

√5+√7 is a not a irrational number

√5+√7 is a rational number

√5+√7=a/b (a, b are co- primes

√7= a/b -√5

Squaring on both sides

(7)square= ( a/b -√5). Square

7 = a square/b square -2.a/b√5+5

2.a/b√5 =a square/b square+5-7

2.a/b √5= a square /b square -2

2.a/b √5=a square-2bsquare/b

square

√5=a square -2 b square / b square× b/2a

√5=a square- 2b square/2ab

This is contruduction

Therefore √5+√7 is an irrational number