Question

which set of numbers includes \\(\sqrt{5}\\)? \\(\bigcirc\\) natural numbers \\(\bigcirc\\) irrational numbers \\(\bigcirc\\) integers \\(\bigcirc\\) rational numbers

Explanation:

Step1: Recall number set definitions

• Natural Numbers: Positive integers (1, 2, 3, ...). $\sqrt{5}\approx2.236$ is not an integer, so not natural.
• Irrational Numbers: Numbers that cannot be expressed as $\frac{p}{q}$ (p, q integers, q≠0), with non - repeating, non - terminating decimals. $\sqrt{5}$ is such a number (since 5 is not a perfect square, its square root has non - repeating, non - terminating decimals).
• Integers: ..., -2, -1, 0, 1, 2, ... $\sqrt{5}$ is not an integer.
• Rational Numbers: Can be expressed as $\frac{p}{q}$ (p, q integers, q≠0). $\sqrt{5}$ cannot be expressed in this form.

Step2: Determine the set for $\sqrt{5}$

From the above analysis, $\sqrt{5}$ belongs to the set of Irrational Numbers.

Answer:

B. Irrational Numbers