Question

Rational and Irrational Numbers Quick Check
4 of 54 of 5 Items
Question
Which statement is true about the square root of 28?(1 point)
Responses

It is between 4 and 5, probably closer to 5.
It is between 4 and 5, probably closer to 5.

It is between 5 and 6, probably closer to 6.
It is between 5 and 6, probably closer to 6.

It is between 5 and 6, probably closer to 5.
It is between 5 and 6, probably closer to 5.

It is between 6 and 7, probably closer to 6.
It is between 6 and 7, probably closer to 6.

Answer 1

To determine the approximate value of \(\sqrt{28}\), we can find the perfect squares around it.

- \(4^2 = 16\)
- \(5^2 = 25\)
- \(6^2 = 36\)

Since \(25 < 28 < 36\), this means that:

\[
5 < \sqrt{28} < 6
\]

Now, we can refine our estimate. We can calculate \(\sqrt{28}\) more specifically:

\[
\sqrt{28} = \sqrt{4 \times 7} = 2\sqrt{7}
\]

To further approximate \(\sqrt{7}\), we note:

\[
2.6^2 = 6.76 \quad \text{and} \quad 2.7^2 = 7.29
\]

So \(\sqrt{7}\) is approximately between \(2.6\) and \(2.7\). Therefore:

\[
2\sqrt{7} \approx 2 \times 2.6 = 5.2 \quad \text{to} \quad 2 \times 2.7 = 5.4
\]

Thus, \(\sqrt{28}\) is approximately between \(5.2\) and \(5.4\), which places it closer to \(5\).

Given this information, the correct statement is:

**It is between 5 and 6, probably closer to 5.**