Question

Determine which two values the following irrational number is between.
V23
A. is between 6.3 and 7.3
B. is between 3.3 and 4.3
C. is between 4.3 and 5.3
D. is between 5.3 and 6.3

Answer 1

To find out where \(\sqrt{23}\) lies, we can first calculate the square of some nearby whole numbers.

Calculating the squares of whole numbers around \(\sqrt{23}\):

- \(4^2 = 16\)
- \(5^2 = 25\)

From this, we can see that:

\[
4 < \sqrt{23} < 5
\]

Next, we can refine our estimates by checking the squares of some decimals:

- \(4.5^2 = 20.25\) (too low)
- \(4.6^2 = 21.16\) (still too low)
- \(4.7^2 = 22.09\) (still too low)
- \(4.8^2 = 23.04\) (too high)

Thus, we find that:

\[
4.7 < \sqrt{23} < 4.8
\]

Now, let's also check the range of \(5.3\) and \(6.3\):

- \(5.3^2 = 28.09\) (too high)
- \(5.4^2 = 29.16\) (too high)

Now let's check if \(\sqrt{23}\) falls between other numbers:

- \(5.0^2 = 25.0\) (too high)

Thus, it's confirmed that:

- \(4.7 < \sqrt{23} < 4.8\), and since both 4.7 and 4.8 fall between 4.3 and 5.3, we can conclude:

Thus,

The correct answer is **C. is between 4.3 and 5.3.**