Question

Between which two consecutive whole numbers does square root of 83 lie fill out the sentence below to justify your answer and use your mouse drag square root of 83 to an approximate correct location on the number line

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Answer 1

since square root of ___ = ___ and square root of ___ = ___ it us known that square root of 83 is between ___ and ___

Answer 2

To determine between which two consecutive whole numbers the square root of 83 lies, we can evaluate the squares of the whole numbers around it.

- \(9^2 = 81\)
- \(10^2 = 100\)

Since \(81 < 83 < 100\), we can conclude that \(9 < \sqrt{83} < 10\).

So, square root of 83 lies between the whole numbers 9 and 10.

You would place \(\sqrt{83}\) on the number line between 9 and 10, closer to 9, since it is approximately \(9.1\).

The sentence would be: "The square root of 83 lies between the whole numbers 9 and 10 because \(9^2 = 81\) and \(10^2 = 100\), and since \(81 < 83 < 100\), it follows that \(9 < \sqrt{83} < 10\)."

Answer 3

Since the square root of \(9^2 = 81\) and the square root of \(10^2 = 100\), it is known that the square root of 83 is between \(9\) and \(10\).