Question

please answer any one question from this​

Answer 1

Answer:

Let √3 + √5 be a rational number , say r

then √3 + √5 = r

On squaring both sides, 

(√3 + √5)2  = r2 

3 + 2 √15 + 5 =  r2  

8 + 2 √15  = r2   

2 √15 =  r2  - 8 

√15 = (r2 - 8) / 2 

Now (r2 - 8) / 2 is a rational number and √15 is an irrational number . 

Since a rational number cannot be equal to an irrational number

Answer 2

Answer:

To show √3+√5 us an irrational number.

First, assume √3+√5 as rational

if √3+√5 is a rational

√3+√5 =a/b(where a and b are co primes)

now,

√3+√5=a/b

√5=a/b-√3

therefore, a/b-√3 is a rational number

and √5 is an irrational number

hence, we know an irrational number is not equal to rational number.

hence, the assumption was wrong.

The contradiction has arising due to wrong assumption.

therefore, √3+√5 is an irrational number.

hence proved.