proximate square root of, 66, end square root
66
66
by following the steps below.
square root of, 66, end square root
66
66
must lie between the whole numbers
and
Answer
Attempt 1 out of 2
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To find the approximate square root of 66, we can use the following steps:
1. Write down the whole numbers that are closest to the square root of 66. The whole numbers closest to the square root of 66 are 8 and 9.
2. Take the square of the smaller whole number (8) and the larger whole number (9). The square of 8 is 64, and the square of 9 is 81.
3. Since 66 is between 64 and 81, the square root of 66 must lie between 8 and 9.
Therefore, the approximate square root of 66 is between 8 and 9.
To one decimal place, square root of, 66, end square root
66
66
must lie between
and
To find the approximate square root of 66 to one decimal place, we need to find the square roots of the closest perfect squares to 66.
The perfect squares closest to 66 are 64 and 81.
The square root of 64 is 8.
The square root of 81 is 9.
Since 66 is between 64 and 81, the square root of 66 must lie between 8 and 9.
Therefore, the approximate square root of 66 to one decimal place is between 8 and 9.
To one decimal place, square root of, 66, end square root
66
66
must lie between
8
8 and
9
9 because 8, squared, equals, start box, 64, end box
8
2
=
64
8
2
=
64
and 9, squared, equals, start box, 81, end box
9
2
=
81
9
2
=
81
, and 66 lies between these values
it was incorrect
Apologies for the incorrect response earlier. Let's correct it.
To find the approximate square root of 66 to one decimal place, we can use a calculator or estimate using some simple calculations:
Let's take the average of 8 and 9:
(8 + 9) / 2 = 8.5
Now, we need to check whether the square of 8.5 is close enough to 66:
8.5^2 = 72.25
Since 72.25 is greater than 66, we need to lower our estimate. Let's try a smaller value.
(8 + 8.5) / 2 = 8.25
Now, we check the square of 8.25:
8.25^2 = 68.0625
Since 68.0625 is still greater than 66, we need to lower our estimate further.
(8 + 8.25) / 2 = 8.125
Now, we check the square of 8.125:
8.125^2 = 66.015625
Here, we have found a square value that is close to 66.015625.
Therefore, the approximate square root of 66 to one decimal place is 8.1.
To two decimal places, square root of, 66, end square root
66
66
must lie between
and
To find the approximate square root of 66 to two decimal places, we can use a calculator or estimation.
Let's start by trying to find whole numbers that are closest to the square root of 66. The closest whole numbers are 8 and 9.
Now, we can check if the square of 8.5 (the average of 8 and 9) is close to 66:
8.5^2 = 72.25
Since 72.25 is greater than 66, we need to lower our estimate. Let's try a smaller value.
Now, we can check if the square of 8.25 (the average of 8 and 8.5) is close to 66:
8.25^2 = 68.0625
Since 68.0625 is still greater than 66, we need to lower our estimate further.
Now, we can check if the square of 8.125 (the average of 8 and 8.25) is close to 66:
8.125^2 = 66.015625
Here, we have found a square value that is close to 66.015625.
Therefore, the approximate square root of 66 to two decimal places is between 8.12 and 8.13.
It has been demonstrated that square root of, 66, end square root
66
66
is between 8.12 and 8.13. If we were to continue this process, it would
because square root of, 66, end square root
66
66
is
.
Submit Answer
Apologies for the confusion in my previous responses. Let's continue the estimation process to find the approximate square root of 66.
From our previous calculations, we determined that the square root of 66 is between 8.12 and 8.13.
To refine our estimate further, let's calculate the square of 8.13:
8.13^2 ≈ 66.2169
Since 66.2169 is greater than 66, we need to lower our estimate. Let's try a smaller value.
Let's calculate the square of 8.12:
8.12^2 ≈ 65.7744
Since 65.7744 is less than 66, we can conclude that the square root of 66 lies between 8.12 and 8.13.
Therefore, the approximate square root of 66 to two decimal places is between 8.12 and 8.13.