Q:(14) Show that V2+V3 is irrational.

1.	Q:(14) Show that V2+V3 is irrational.
Answer» He please tell me simplest answer of this question Let us assume that √2 + √3 is a rational number Thus,√2 + √3 = (a/b) where a and b are co-prime numbers On squaring both sides , we get2 + 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, our contradiction is wrong.So, (√2 + √3) is an irrational no.

Answer»

He please tell me simplest answer of this question

Let us assume that √2 + √3 is a rational number

Thus,√2 + √3 = (a/b) where a and b are co-prime numbers

On squaring both sides , we get2 + 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, our contradiction is wrong.So, (√2 + √3) is an irrational no.

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