Question

√2+√3 is rational or irrational number​

Answer 1

Answer:

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√2+√3 is irrational number

Answer 2

Answer:

√2+√3 is an irrational number.

We can also prove this:

Let us assume that √2+√3 is rational.

Therefore, √2+√3 = a/b where a and b are integers and b is not equal to zero.

√2+√3 = a/b

√2 = a/b - √3

Now, squaring both sides, we get

(√2)^2 = a^2/b^2 + 3 - 2 × a/b × √3

=> 2 = a^2/b^2 + 3 - 2 × a/b × √3

We get,

2a/b × √3 = a^2/b^2 + 3 - 2

= a^2/b^2 + 1

=> √3 = (a^2 + b^2)/2ab

Since, a and b are integers, (a^2 + b^2)/2ab is rational, so √3 is rational.

But this contradicts the fact that √3 is irrational.

Hence, √2+√3 is irrational.