To find the value of [tex]\(\sqrt{42}\)[/tex] and its classification, we need to follow a few steps:
1. Determine if [tex]\(\sqrt{42}\)[/tex] is a rational number:
- A rational number can be expressed as a fraction [tex]\(\frac{p}{q}\)[/tex] where [tex]\(p\)[/tex] and [tex]\(q\)[/tex] are integers and [tex]\(q \neq 0\)[/tex].
- The value of [tex]\(\sqrt{42}\)[/tex] is approximately 6.48074069840786.
- Since 6.48074069840786 cannot be expressed exactly as a fraction of two integers, [tex]\(\sqrt{42}\)[/tex] is an irrational number.
2. Identify the value between which [tex]\(\sqrt{42}\)[/tex] lies:
- To find the range, we need to look at the integer part and the next integer value.
- The integer part of 6.48074069840786 is 6.
- The next integer value is 7.
- Therefore, [tex]\(\sqrt{42}\)[/tex] lies between 6 and 7.
So, the correct answers in the drop-down menus should be:
- The value of [tex]\(\sqrt{42}\)[/tex] is an irrational number.
- Its value is between 6 and 7.
