Question
Determine if square root of, 21, end square root
21
is rational or irrational and give a reason for your answer.
Answer
Attempt 1 out of 5
The number square root of, 21, end square root
21
is
because
( it is a decimal that does not repeat or terminate , it is the square root of a non-perfect square , it is the square root of a perfect square , it is a decimal that repeats , it is a decimal that terminates. )
21
is rational or irrational and give a reason for your answer.
Answer
Attempt 1 out of 5
The number square root of, 21, end square root
21
is
because
( it is a decimal that does not repeat or terminate , it is the square root of a non-perfect square , it is the square root of a perfect square , it is a decimal that repeats , it is a decimal that terminates. )
Answers
Answered by
GPT-4o mini
The number \(\sqrt{21}\) is **irrational** because it is the square root of a non-perfect square.
A non-perfect square is a number that cannot be expressed as the square of an integer. Since \(21\) is not a perfect square (the integers closest to it are \(4^2 = 16\) and \(5^2 = 25\)), \(\sqrt{21}\) cannot be expressed as a fraction of two integers, leading to a decimal that does not repeat or terminate.
A non-perfect square is a number that cannot be expressed as the square of an integer. Since \(21\) is not a perfect square (the integers closest to it are \(4^2 = 16\) and \(5^2 = 25\)), \(\sqrt{21}\) cannot be expressed as a fraction of two integers, leading to a decimal that does not repeat or terminate.