Questions: Select all true statements about √56. It is a rational number. It is a real number. It is an integer. It is an irrational number. It is not a real number.

Solution Steps

To determine which statements about \(\sqrt{56}\) are true, we need to evaluate its properties:

1. Check if \(\sqrt{56}\) is a rational number.
2. Check if \(\sqrt{56}\) is a real number.
3. Check if \(\sqrt{56}\) is an integer.
4. Check if \(\sqrt{56}\) is an irrational number.
5. Check if \(\sqrt{56}\) is not a real number.

A rational number can be expressed as the quotient of two integers. The value of \(\sqrt{56}\) is approximately 7.483. Since this value cannot be expressed as a simple fraction of two integers, \(\sqrt{56}\) is not a rational number.

A real number is any value that can represent a distance along a line. Since \(\sqrt{56} \approx 7.483\) is a well-defined number on the real number line, \(\sqrt{56}\) is a real number.

An integer is a whole number without any fractional or decimal part. Since \(\sqrt{56} \approx 7.483\) is not a whole number, \(\sqrt{56}\) is not an integer.

An irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion. Since \(\sqrt{56}\) is not rational and its decimal expansion is non-repeating and non-terminating, \(\sqrt{56}\) is an irrational number.

Since we have already established that \(\sqrt{56}\) is a real number, it is incorrect to say that \(\sqrt{56}\) is not a real number.

Final Answer