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

select the correct choice below and fill in any answer boxes in your choice.

a. \\(\sqrt{53} = \\)
(type an integer or decimal rounded to two decimal places as needed.)
b. the square root is not a real number.

Explanation:

⚡ Using what you learned: Real Number System Overview

Step 1: Classify the number

The number is \(\sqrt{53}\).

• Since \(53\) is a positive number, its square root is a real number.
• Since \(53\) is not a perfect square (the closest perfect squares are \(49 = 7^2\) and \(64 = 8^2\)), its square root cannot be written as a terminating or repeating decimal, nor as a fraction of two integers.

Therefore, \(\sqrt{53}\) is an irrational number.

Step 2: Approximate the value

To find the decimal approximation of \(\sqrt{53}\) rounded to two decimal places:

$$ \sqrt{53} \approx 7.28010989... $$

Rounding to two decimal places gives:

$$ \sqrt{53} \approx 7.28 $$

Answer:

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

irrational

• Select the correct choice below and fill in any answer boxes in your choice:

A. \(\sqrt{53} = 7.28\)