Question
Approximate square root of, 46, end square root
46
square root of, 46, end square root
46
must lie between the whole numbers
6
6 and
7
7 because 6, squared, equals, start box, 36, end box6
2
=
36
and 7, squared, equals, start box, 49, end box7
2
=
49
, and 46 lies between these values.
Drag square root of, 46, end square root
46
based on your estimate above:
Real
√46
__
_
To one decimal place, square root of, 46, end square root
46
must lie between
6.7
6.7 and
6.8
6.8 because 6, point, 7, squared, equals, start box, 44, point, 8, 9, end box6.7
2
=
44.89
and 6, point, 8, squared, equals, start box, 46, point, 2, 4, end box6.8
2
=
46.24
, and 46 lies between these values.
Drag square root of, 46, end square root
46
based on your estimate above:
Real
√46
__
_
To two decimal places, square root of, 46, end square root
46
must lie between
6.78
6.78 and
6.79
6.79 because 6, point, 7, 8, squared, equals, start box, 45, point, 9, 6, 8, 4, end box6.78
2
=
45.9684
and 6, point, 7, 9, squared, equals, start box, 46, point, 1, 0, 4, 1, end box6.79
2
=
46.1041
, and 46 lies between these values.
Drag square root of, 46, end square root
46
based on your estimate above:
Real
√46
__
_
Answer
Attempt 1 out of 2
It has been demonstrated that square root of, 46, end square root
46
is between 6.78 and 6.79. If we were to continue this process, it would
because square root of, 46, end square root
46
is
.
46
square root of, 46, end square root
46
must lie between the whole numbers
6
6 and
7
7 because 6, squared, equals, start box, 36, end box6
2
=
36
and 7, squared, equals, start box, 49, end box7
2
=
49
, and 46 lies between these values.
Drag square root of, 46, end square root
46
based on your estimate above:
Real
√46
__
_
To one decimal place, square root of, 46, end square root
46
must lie between
6.7
6.7 and
6.8
6.8 because 6, point, 7, squared, equals, start box, 44, point, 8, 9, end box6.7
2
=
44.89
and 6, point, 8, squared, equals, start box, 46, point, 2, 4, end box6.8
2
=
46.24
, and 46 lies between these values.
Drag square root of, 46, end square root
46
based on your estimate above:
Real
√46
__
_
To two decimal places, square root of, 46, end square root
46
must lie between
6.78
6.78 and
6.79
6.79 because 6, point, 7, 8, squared, equals, start box, 45, point, 9, 6, 8, 4, end box6.78
2
=
45.9684
and 6, point, 7, 9, squared, equals, start box, 46, point, 1, 0, 4, 1, end box6.79
2
=
46.1041
, and 46 lies between these values.
Drag square root of, 46, end square root
46
based on your estimate above:
Real
√46
__
_
Answer
Attempt 1 out of 2
It has been demonstrated that square root of, 46, end square root
46
is between 6.78 and 6.79. If we were to continue this process, it would
because square root of, 46, end square root
46
is
.
Answers
GPT-4o mini
To summarize the findings you've made about the square root of 46, we can break it down as follows:
1. **Estimate**:
- You correctly determined that \(\sqrt{46}\) lies between the whole numbers 6 and 7, since \(6^2 = 36\) and \(7^2 = 49\).
2. **More precise estimate**:
- You then narrowed it down to between 6.7 and 6.8 because:
- \(6.7^2 = 44.89\)
- \(6.8^2 = 46.24\)
3. **Even more precise estimate**:
- Finally, you assessed that \(\sqrt{46}\) lies between 6.78 and 6.79 because:
- \(6.78^2 = 45.9684\)
- \(6.79^2 = 46.1041\)
Conclusively, you have shown that \(\sqrt{46}\) is indeed between 6.78 and 6.79. If you were to continue this process, you could further narrow it down.
4. **Conclusion**:
- Based on your calculations, the value of \(\sqrt{46}\) is approximately **6.782** (to three decimal places) or could be presented as \(6.78\) when rounded to two decimal places.
You can state:
"If we were to continue this process, it would provide a more precise approximation of \(\sqrt{46}\) because \(\sqrt{46}\) is between 6.78 and 6.79."
For practical purposes, the approximate value of \(\sqrt{46}\) is **approximately 6.78** (to two decimal places).
1. **Estimate**:
- You correctly determined that \(\sqrt{46}\) lies between the whole numbers 6 and 7, since \(6^2 = 36\) and \(7^2 = 49\).
2. **More precise estimate**:
- You then narrowed it down to between 6.7 and 6.8 because:
- \(6.7^2 = 44.89\)
- \(6.8^2 = 46.24\)
3. **Even more precise estimate**:
- Finally, you assessed that \(\sqrt{46}\) lies between 6.78 and 6.79 because:
- \(6.78^2 = 45.9684\)
- \(6.79^2 = 46.1041\)
Conclusively, you have shown that \(\sqrt{46}\) is indeed between 6.78 and 6.79. If you were to continue this process, you could further narrow it down.
4. **Conclusion**:
- Based on your calculations, the value of \(\sqrt{46}\) is approximately **6.782** (to three decimal places) or could be presented as \(6.78\) when rounded to two decimal places.
You can state:
"If we were to continue this process, it would provide a more precise approximation of \(\sqrt{46}\) because \(\sqrt{46}\) is between 6.78 and 6.79."
For practical purposes, the approximate value of \(\sqrt{46}\) is **approximately 6.78** (to two decimal places).