Question

Using a number line, what whole number and rational number to the nearest half is the square root of 32 between?
a) 6.5, 6.7
b) 6, 7
c) 5.5, 6
d) 5, 5.5

Answer 1

umm less words and symbols

Answer 2

To find the whole number and rational number to the nearest half that the square root of 32 falls between, we first calculate \(\sqrt{32}\).

We can simplify \(\sqrt{32}\):

\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}
\]

The approximate value of \(\sqrt{2}\) is about 1.414. Therefore:

\[
4\sqrt{2} \approx 4 \times 1.414 \approx 5.656
\]

Now, we want to determine the numbers between which \(5.656\) falls:

- The whole number just less than \(5.656\) is \(5\).
- The whole number just greater than \(5.656\) is \(6\).

Now we also check the rational number to the nearest half:

The nearest half to \(5.656\) is \(5.5\).

Putting it all together, we can conclude that \(\sqrt{32}\) is between \(5.5\) and \(6\).

Thus, the answer is:

**c) 5.5, 6**

Answer 3

\(\sqrt{32} \approx 5.656\)

It is between:

- Whole numbers: \(5\) and \(6\)
- Nearest half: \(5.5\) and \(6\)

So the answer is:

**c) 5.5, 6**