Question

prove that √2+√3 are irrational numbers​

Answer 1

Let √2 + √3 = (a/b) is a rational no. On squaring both sides , we get 2 + 3 + 2√6 = (a2/b2) So,5 + 2√6 = (a2/b2) a rational no. So, 2√6 = (a2/b2) – 5 Since, 2√6 is an irrational no. and (a2/b2) – 5 is a rational no. So, my contradiction is wrong. So, (√2 + √3) is an irrational no.

Answer 2

Answer:

TO PROOF √2+√3 IS IRRATIONAL

Step-by-step explanation:

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

√2+√3=p/q [p and q are co-prime numbers]

so, √2=p/q+√3

after simplifying we get

√2=p+√3q/q

now we know that,  

√2 is an irrational number

p+√3q/q is a rational number

BUT A IRRATIONAL NUMBER IS NOT EQUAL TO A RATIONAL NUMBER

this contradiction arrived due to our wrong assumption that √2+√3 is rational

Therefore √2+√3 is an irrational number