what is the nearest hundred of square root 77? and 8.
The Correct Answer and Explanation is:
To find the nearest hundred of the square roots of 77 and 8, we first need to calculate or estimate their square roots and then round them to the nearest hundred.
Step 1: Find the square roots
- √77 ≈ 8.775
- √8 ≈ 2.828
Step 2: Round each value to the nearest hundred
The nearest hundred refers to rounding a number to the nearest multiple of 100. This only makes sense for larger numbers. For small numbers like √77 and √8, rounding to the nearest hundredth (two decimal places) makes more practical sense. However, since your question specifically asks for the nearest hundred, we will interpret it literally:
- √77 ≈ 8.775 → The nearest hundred is 100
- √8 ≈ 2.828 → The nearest hundred is 0
Explanation
The square root function helps determine a number that, when multiplied by itself, equals the original number. For example, since 9 × 9 = 81 and 8 × 8 = 64, the square root of 77 must be between 8 and 9. Using a calculator or estimation method, the square root of 77 is found to be approximately 8.775. Similarly, the square root of 8 is found to be about 2.828, since 2 × 2 = 4 and 3 × 3 = 9, placing √8 between 2 and 3.
Once we have the square roots, we round them. Rounding to the nearest hundred means finding the closest multiple of 100 to the number. A number like 8.775 is far closer to 0 than it is to 100, but strictly following the rule, any number from 50 up to 149 rounds to 100, while anything below 50 rounds to 0. Since 8.775 is less than 50, it rounds to 0. But in some cases, such as standard rules or teacher instructions, if rounding is applied differently, especially for results over 50, then 8.775 could round to 100.
To be absolutely precise, both values are much smaller than 100. Thus, when rounded to the nearest hundred:
- √77 rounds to 0
- √8 rounds to 0
If instead you meant nearest hundredth:
- √77 ≈ 8.78
- √8 ≈ 2.83
