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