To solve the problem of rounding [tex]\(\sqrt{6}\)[/tex] to two decimal places, let's proceed with the following steps:
1. Calculate the square root of 6: First, we need to determine the value of [tex]\(\sqrt{6}\)[/tex].
2. Identify the numerical value: The square root of 6, when calculated, gives us approximately 2.449489742783178.
3. Round to two decimal places: Next, we need to round this value to two decimal places. When rounding to two decimal places, we look at the third decimal place to decide whether to round up or down.
- If the third decimal place is 5 or more, increase the second decimal place by one.
- If the third decimal place is less than 5, keep the second decimal place as it is.
In this case, the third decimal place is 9.
4. Apply rounding rule: Since the third decimal place (9) is greater than 5, we round up the second decimal place:
- The value 2.449 becomes 2.45 when rounded to two decimal places.
Therefore, the value of [tex]\(\sqrt{6}\)[/tex] rounded to two decimal places is [tex]\(\mathbf{2.45}\)[/tex].
