Between which two consecutive whole numbers does square root of, 54, end square root

Question

54
​
lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 54, end square root
54
​
to an approximately correct location on the number line.
Real
√54
__
_
Answer
Attempt 1 out of 2

Since square root of, end square root
2
2
​

​

equals=
and square root of, end square root
2
2
​

​

equals=
it is known that square root of, 54, end square root
54
​
is between
and
.

Answer 1

To determine between which two consecutive whole numbers the square root of 54 lies, we can first find the whole numbers that are perfect squares around that value.

1. First, we know that:

   • \(7^2 = 49\)
   • \(8^2 = 64\)

2. Thus, it is apparent that:

   • \(49 < 54 < 64\)

3. Taking the square root of these inequalities, we get:

   • \(7 < \sqrt{54} < 8\)

Therefore, we can fill out the sentence as follows:

Since \( \sqrt{49} = 7 \) and \( \sqrt{64} = 8 \), it is known that \( \sqrt{54} \) is between 7 and 8.

Now, you can place \( \sqrt{54} \) approximately on the number line between the two numbers, leaning more towards 7.

So in summary:

• The square root of 54 is between 7 and 8.