Question

Prove that
√2 +
√3 is irrational​

Answer 1

Answer:

The answer can be given as below.

Step-by-step explanation:

Answer 2

here is your answer mate:

Let us assume that √2  is rational. then there exists integers a and b such that

√2  = a/b (where a and b are co prime)

squaring on both sides

2 = a^2/b^2

2b^2 = a^2 - (i)

2 divides a^2

thus 2 divides a - (ii)

a = 2c

a^2 = 4c^2

2b^2 = 4c^2 - from (i)

b^2 = 2c^2

2 divides b^2

thus 2 divides b -(iii)

from ii and iii

2 is the common factor of a and b

but that is not possible as a and b are co prime

thus our assumption is wrong

thus √2 is irrational - iv

let us assume that √2 + √3 is rational

√2 + √3 = a/b (where a and b are co prime)

√3 = a/b - √2

squaring on both sides

3= a^2/b^2 - 2a√2/b + 2

a^2/b^2 - 1 = 2a√2/b

a^2 - b^2/2ab = √2

since a and b are integers

LHS is rational

thus √2 should be rational

but we know that √2 is irrational

hence our assumption is wrong

√2 + √3 is irrational

hope this helps you buddy

please mark as brainliest:-)