Estimate the value of 6×2–√. Which of the following choices is the best estimate?(1 point)
The value of 6×2–√ cannot be determined without further information.
8.4
9.8
6.4
7.1?
The best estimate for the value of 6×2–√ is 6.4.
Which statement is true about the square root of 28?(1 point)
It is between 6 and 7, probably closer to 6.
It is between 5 and 6, probably closer to 6.
It is between 4 and 5, probably closer to 5.
It is between 5 and 6, probably closer to 5.
The statement that is true about the square root of 28 is "It is between 5 and 6, probably closer to 5."
To estimate the value of 6×2–√, we can first calculate 6×2, which equals 12. Then we subtract the square root (√) of a number, which is not specified in the question. Since the value inside the square root is unknown, we cannot accurately estimate the value. Therefore, none of the given choices can be considered the best estimate.
To estimate the value of 6×2–√, we need to perform the calculation and then round to the nearest whole number. Let's break it down step by step:
Step 1: Calculate 6×2 to get 12.
Step 2: Calculate the square root of a number. If we assume it to be the square root of 2 (√2), then the approximate value is 1.414.
Step 3: Subtract the square root from the product obtained in Step 1: 12 - 1.414 = 10.586.
Now, we need to choose the best estimate from the following options:
a) 10.6
b) 12
c) 11
d) 9
Comparing the result we obtained (10.586) with the available choices:
a) 10.6: The correct rounded value to the nearest tenth is 10.6, which is close to our result.
b) 12: This option is the exact value of our initial calculation, but it is not an estimate.
c) 11: This option is closest to our result when rounding to the nearest whole number, but it is still not as accurate as option a).
d) 9: This option is far from the actual result obtained, so it is not a good estimate.
Hence, the best estimate for the value of 6×2–√ is 10.6, which corresponds to choice a).