Is the number \/6+3 rational or irrational?

Answer 1

To determine whether the expression \(\sqrt{6} + 3\) is rational or irrational, we start by analyzing the components.

1. Identify \(\sqrt{6}\): The square root of 6 is an irrational number because it cannot be expressed as a fraction of two integers. In general, the square root of any non-perfect square is irrational.

2. Addition of Rational and Irrational Numbers: The number \(3\) is a rational number (it can be expressed as \(\frac{3}{1}\)). When you add a rational number to an irrational number, the result is always irrational.

Therefore, since \(\sqrt{6}\) is irrational and \(3\) is rational, the sum \(\sqrt{6} + 3\) is also irrational.

In conclusion, \(\sqrt{6} + 3\) is an irrational number.