Question

Determine if square root of, 53, end square root
53
​
is rational or irrational and give a reason for your answer.
Answer
Attempt 1 out of 2

The number square root of, 53, end square root
53
​
is
because

Answer 1

The square root of 53 is irrational because it cannot be expressed as a fraction of two integers. A number is considered rational if it can be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

To determine if \( \sqrt{53} \) is rational, we can check if 53 is a perfect square. The integer 53 is not a perfect square since the integers closest to its square root are 7 (\(7^2 = 49\)) and 8 (\(8^2 = 64\)). Therefore, \( \sqrt{53} \) does not simplify to a rational number.

In conclusion, the number \( \sqrt{53} \) is irrational because it cannot be expressed as a fraction of two integers.