Between which two consecutive whole numbers does square root of, 23, end square root
23
23
lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 23, end square root
23
23
to an approximately correct location on the number line.
The square root of 23 lies between 4 and 5.
To justify this answer, we can calculate the square of the whole numbers to find the range in which the square root of 23 falls:
4^2 = 16
5^2 = 25
Since the square root of 23 is greater than the square root of 16 (which is 4) and less than the square root of 25 (which is 5), it lies between 4 and 5.
On the number line, you can place the square root of 23 approximately halfway between 4 and 5.
Since square root of, empty space, end square root
2
2
equals
=
=
and square root of, empty space, end square root
2
2
equals
=
=
it is known that square root of, 23, end square root
23
23
is between
and
Since the square root of 2 is approximately 1.41 and the square root of 3 is approximately 1.73, it is known that the square root of 23 is between 4.8 and 4.9.
Between which two consecutive whole numbers does square root of, 23, end square root
23
23
lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 23, end square root
23
23
to an approximately correct location on the number line.
Real
√23
__
_
Answer
Attempt 2 out of 2
Since square root of, empty space, end square root
2
2
equals
=
=
and square root of, empty space, end square root
2
2
equals
=
=
it is known that square root of, 23, end square root
23
23
is between
and
.
Since the square root of 4 is 2 and the square root of 25 is 5, it is known that the square root of 23 is between 4 and 5.
On the number line, you can place the square root of 23 approximately between 4 and 5, closer to 5.
To determine between which two consecutive whole numbers the square root of 23 lies, we can calculate its approximate value. The square root of 23 is approximately 4.795. Since 23 is closer to the square of 5 than the square of 4, we can conclude that the square root of 23 lies between the consecutive whole numbers 4 and 5.
To find between which two consecutive whole numbers the square root of 23 lies, we can calculate the square root of 23 using a calculator or mathematical methods.
Using a calculator, we can find that the square root of 23 is approximately 4.7958.
Now, let's determine the two consecutive whole numbers between which the square root of 23 lies.
We know that the square of any whole number is always greater than the number itself and the square root is the inverse of squaring. Therefore, if we square a number greater than 4.7958, it will be greater than 23.
If we square 5, we get 25, which is greater than 23.
Therefore, the square root of 23 lies between 4 and 5.
Now, you can drag the square root of 23, approximately 4.7958, to a location between 4 and 5 on the number line.