Question

determine whether \\(\sqrt{53}\\) is rational, irrational, or not a real number.

is \\(\sqrt{53}\\) rational, irrational, or not a real number?

• not a real number
• rational
• irrational

Explanation:

⚡ Using what you learned: Real Number System Overview

Step 1: Check if the number is real

A square root of a non-negative number is always a real number. Since \(53 \ge 0\), \(\sqrt{53}\) is a real number.

Step 2: Determine if it is rational or irrational

A square root of an integer is rational only if the integer is a perfect square.

We check the perfect squares near \(53\):

$$ 7^2 = 49 $$

$$ 8^2 = 64 $$

Since \(53\) lies between \(49\) and \(64\), it is not a perfect square. Therefore, its square root cannot be written as a fraction of two integers, making \(\sqrt{53}\) an irrational number.

Answer:

irrational