Question

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.

Answer 1

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

Answer 2

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
.

Answer 3

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.

Answer 4

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.

Answer 5

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.