Question

question
determine if \\(\sqrt{35}\\) is rational or irrational and give a reason for your answer.

answer attempt 1 out of 2

the number \\(\sqrt{35}\\) is     because

Explanation:

Step1: Recall rational number definition

A rational number can be expressed as $\frac{p}{q}$ where $p,q$ are integers, $q
eq0$, and $p,q$ have no common factors other than 1 (in lowest terms). Also, a rational number's square root is rational only if the number is a perfect square.

Step2: Check if 35 is a perfect square

Factorize 35: $35 = 5\times7$. Neither 5 nor 7 are perfect squares, and there's no integer $n$ such that $n^2 = 35$ (since $5^2 = 25$ and $6^2 = 36$). So $\sqrt{35}$ cannot be expressed as a fraction of two integers, hence it's irrational.

Answer:

The number $\sqrt{35}$ is irrational because 35 is not a perfect square (and thus $\sqrt{35}$ cannot be expressed as a ratio of two integers).