Between which two consecutive whole numbers does square root of, 78, end square root

Question

78
​
lie? Fill out the sentence below to justify your answer and use your mouse to drag square root of, 78, end square root
78
​
to an approximately correct location on the number line.
Real
√78
__
_
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, 78, end square root
78
​
is between
and
.

Answer 1

To determine between which two consecutive whole numbers \(\sqrt{78}\) lies, we can calculate the perfect squares around 78.

• The perfect square just below 78 is \(8^2 = 64\).
• The perfect square just above 78 is \(9^2 = 81\).

Since \(64 < 78 < 81\), we have:

\[ 8 < \sqrt{78} < 9 \]

Thus, we can fill out the sentence as follows:

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Real \( \sqrt{78} \) lies between 8 and 9.

Since \( \sqrt{64} = 8 \) and \( \sqrt{81} = 9 \), it is known that \( \sqrt{78} \) is between 8 and 9.

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For the number line visualization, you would place \(\sqrt{78}\) between 8 and 9, closer to 8 (as \(\sqrt{78}\) is approximately 8.83).