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.
Transcript text: Select all true statements about $\sqrt{56}$.
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
Solution Steps
To determine which statements about 56 are true, we need to evaluate its properties:
Check if 56 is a rational number.
Check if 56 is a real number.
Check if 56 is an integer.
Check if 56 is an irrational number.
Check if 56 is not a real number.
Step 1: Evaluate if 56 is a rational number
A rational number can be expressed as the quotient of two integers. The value of 56 is approximately 7.483. Since this value cannot be expressed as a simple fraction of two integers, 56 is not a rational number.
Step 2: Evaluate if 56 is a real number
A real number is any value that can represent a distance along a line. Since 56≈7.483 is a well-defined number on the real number line, 56 is a real number.
Step 3: Evaluate if 56 is an integer
An integer is a whole number without any fractional or decimal part. Since 56≈7.483 is not a whole number, 56 is not an integer.
Step 4: Evaluate if 56 is an irrational number
An irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion. Since 56 is not rational and its decimal expansion is non-repeating and non-terminating, 56 is an irrational number.
Step 5: Evaluate if 56 is not a real number
Since we have already established that 56 is a real number, it is incorrect to say that 56 is not a real number.