Question

prove that✓5+✓3 is an irrational no​

Answer 1

Hello friend....

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 . Our assumption that √3 + √5 is rational wrong .

Hope helps