Question

3+2√5is irrational prove that if √5is irrational​

Answer 1

Answer:

HERE IS UR ANSWER...............

Answer 2

Answer:

hope this helps you...... i have tried it on my way........please comment and let me know

Step-by-step explanation:

let us assume that √5 a rational number

$\sqrt{5}$ = a/b                where a & b are co primes and b ≠ 0

(squaring both sides)

5 = a²/b²

5b² = a²

(5 can divide a & a²)

(a = 5c )

5b² = (5c)²  

5b² = 25c²

b² = 25c²/5

b² = 5c²

(5 divides b & b²)

∴ √5 is a rational number and a & b are its factors

but this contradicts the fact that a & b are co primes

∴ our assumption was wrong √5 is an irrational number

let us assume that 3+2√5 is a rational number

3+2√5 = a/b   (where a & b are co primes and b ≠ 0)

2√5 = a/b -3

2√5 = a-3b/b

√5 = 2a-3b/b

∴√5 is a rational number and 3+2√5 is also a rational number

but this contradicts the fact that √5 is an irrational number

∴ our assumption was wrong , 3+2√5 is an irrational number