Question
Determine if sqrt(35) is rational or irrational and give a reason for your answer.
Answer Attempt 1 out of 2
The number sqrt(35) is because
Answer Attempt 1 out of 2
The number sqrt(35) is because
Answers
Answered by
GPT-4o mini
The number \(\sqrt{35}\) is irrational because it cannot be expressed as a fraction of two integers.
To determine whether \(\sqrt{35}\) is rational or irrational, we first check whether \(35\) is a perfect square. The perfect squares around \(35\) are \(25\) (which is \(5^2\)) and \(36\) (which is \(6^2\)). Since \(35\) is not equal to either \(25\) or \(36\), it is not a perfect square.
Furthermore, we can prove that \(\sqrt{35}\) is irrational by using the fact that if \(\sqrt{n}\) is rational, \(n\) must be a perfect square. Since \(35\) is not a perfect square, this implies that \(\sqrt{35}\) is irrational.
In summary, \(\sqrt{35}\) is irrational because it cannot be expressed as a fraction \(\frac{a}{b}\) where \(a\) and \(b\) are integers (and \(b \neq 0\)).
To determine whether \(\sqrt{35}\) is rational or irrational, we first check whether \(35\) is a perfect square. The perfect squares around \(35\) are \(25\) (which is \(5^2\)) and \(36\) (which is \(6^2\)). Since \(35\) is not equal to either \(25\) or \(36\), it is not a perfect square.
Furthermore, we can prove that \(\sqrt{35}\) is irrational by using the fact that if \(\sqrt{n}\) is rational, \(n\) must be a perfect square. Since \(35\) is not a perfect square, this implies that \(\sqrt{35}\) is irrational.
In summary, \(\sqrt{35}\) is irrational because it cannot be expressed as a fraction \(\frac{a}{b}\) where \(a\) and \(b\) are integers (and \(b \neq 0\)).
There are no human answers yet. A form for humans to post answers is coming very soon!