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.

1 answer

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.