Approximate square root of, 37, end square root
37
37
by following the steps below.
square root of, 37, end square root
37
37
must lie between the whole numbers
and
6 and 7.
To approximate the square root of 37, we can use the following steps:
1. Take the average of the two whole numbers: (6 + 7) / 2 = 6.5
2. Square the average: 6.5 x 6.5 = 42.25
3. Compare the squared average to the original number. Since 42.25 is greater than 37, the square root of 37 must be less than 6.5.
4. Repeat steps 1-3, but now using the lower whole number as the new upper limit: (6 + 6.5) / 2 = 6.25. Square 6.25 to get 39.0625.
5. Compare 39.0625 to 37. Since 39.0625 is greater than 37, the square root of 37 must be less than 6.25.
6. Repeat steps 1-3 once more, now using the lower whole number as the new upper limit: (6 + 6.25) / 2 = 6.125. Square 6.125 to get 37.515625.
7. Compare 37.515625 to 37. Since 37.515625 is slightly greater than 37, the square root of 37 must be somewhere between 6.125 and 6.25.
Therefore, the approximate square root of 37 is between 6.125 and 6.25.
Approximate square root of, 37, end square root
37
37
by following the steps below.
square root of, 37, end square root
37
37
must lie between the whole numbers
6
6 and
7
7 because 6, squared, equals, start box, 36, end box
6
2
=
36
6
2
=
36
and 7, squared, equals, start box, 49, end box
7
2
=
49
7
2
=
49
, and 37 lies between these values.
Drag square root of, 37, end square root
37
37
based on your estimate above:
Real
√37
__
_
To one decimal place, square root of, 37, end square root
37
37
must lie between
and
6.1 and 6.2.
To further approximate the square root of 37, we can use the following steps:
1. Take the average of the two values found in the previous approximation: (6.125 + 6.25) / 2 = 6.1875
2. Square the average: 6.1875 x 6.1875 = 38.31640625
3. Compare the squared average to the original number. Since 38.31640625 is greater than 37, the square root of 37 must be less than 6.1875.
4. Repeat steps 1-3, but now using the lower value as the new upper limit: (6.125 + 6.1875) / 2 = 6.15625. Square 6.15625 to get 37.925537109375.
5. Compare 37.925537109375 to 37. Since 37.925537109375 is slightly greater than 37, the square root of 37 must be somewhere between 6.15625 and 6.1875.
Therefore, the approximate square root of 37 is between 6.15625 and 6.1875. To one decimal place, it must lie between 6.1 and 6.2.
To one decimal place, square root of, 37, end square root
37
37
must lie between
and
because 6, squared, equals, start box, 36, end box
6
2
=
36
6
2
=
36
and 6, point, 2, squared, equals, start box, 38, point, 44, end box
6.
2
2
=
38.44
6.2
2
=
38.44
, and 37 lies between these values.
To one decimal place, the square root of 37 lies between 6.0 and 6.2.
Approximate square root of, 37, end square root
37
37
by following the steps below.
square root of, 37, end square root
37
37
must lie between the whole numbers
6
6 and
7
7 because 6, squared, equals, start box, 36, end box
6
2
=
36
6
2
=
36
and 7, squared, equals, start box, 49, end box
7
2
=
49
7
2
=
49
, and 37 lies between these values.
Drag square root of, 37, end square root
37
37
based on your estimate above:
Real
√37
__
_
To one decimal place, square root of, 37, end square root
37
37
must lie between
and
because 6, point, 1, squared, equals, start box, 37, point, 21, end box
6.
1
2
=
37.21
6.1
2
=
37.21
and 6, point, 2, squared, equals, start box, 38, point, 44, end box
6.
2
2
=
38.44
6.2
2
=
38.44
, and 37 lies between these values.