Determine if square root of, 21, end square root

Question

21
​
is rational or irrational and give a reason for your answer.
Answer
Attempt 1 out of 2

The number square root of, 21, end square root
21
​
is
because

Answer 1

The square root of 21 is irrational because it cannot be expressed as a fraction of two integers.

To explain further, a number is considered rational if it can be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). The square root of 21 is not a perfect square (the perfect squares near it are 16 and 25), and it cannot be simplified to a fraction of two integers.

Since 21 does not have any integer factors that are perfect squares, its square root does not resolve into a simple fraction, confirming that \( \sqrt{21} \) is irrational.