Determine if square root of, 73, end square root

Question

73
​
is rational or irrational and give a reason for your answer.
Answer
Attempt 1 out of 2

The number square root of, 73, end square root
73
​
is
because

Answer 1

The number \( \sqrt{73} \) is irrational because it cannot be expressed as a fraction of two integers. A number is classified as irrational if it cannot be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \) is not zero.

To prove that \( \sqrt{73} \) is irrational, we can note that 73 is not a perfect square; the integers \( 8^2 = 64 \) and \( 9^2 = 81 \) are the closest perfect squares to 73. Since no integer squared equals 73, \( \sqrt{73} \) cannot be expressed as a simple fraction, confirming that it is irrational.

Answer: The number \( \sqrt{73} \) is irrational because it cannot be expressed as a fraction of two integers.