Which statement is true about the square root of 28?(1 point) Responses It is between 5 and 6, probably closer to 6. It is between 5 and 6, probably closer to 6. It is between 6 and 7, probably closer to 6. It is between 6 and 7, probably closer to 6. 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 5.

1 answer

To determine the square root of 28, we can find the perfect squares around it.

  • The square of 5 is \(5^2 = 25\).
  • The square of 6 is \(6^2 = 36\).

Since 28 is between 25 and 36, we know that:

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

Next, we can approximate \(\sqrt{28}\). Since 28 is closer to 25 than to 36, we would expect \(\sqrt{28}\) to be closer to 5 than to 6.

To calculate it more accurately, we can recognize that:

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

Approximating \(\sqrt{7}\), we know that:

  • \(2.6^2 = 6.76\),
  • \(2.7^2 = 7.29\).

Thus, \(2.6 < \sqrt{7} < 2.7\), which gives:

\[ 5.2 < 2\sqrt{7} < 5.4. \]

Therefore, we can conclude that \(\sqrt{28}\) is between 5 and 6, and we expect it to be closer to 5.

Thus, the correct statement is:

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