Question

prove that √3 + √5 is irrational.



its very imp.. pls give ans ​

Answer 1

Answer:

hey dude here is your 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 . Our assumption that √3 + √5 is rational wrong .

it means√3+√5 is irrational

hence proved

i hope my answer help you

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Answer 2

Answer:

Step-by-step explanation:

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 .

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