Which statement is true about the square root of 28?(1 point)

Responses

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

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

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

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

1 answer

To determine the approximate value of the square root of 28, we will consider the perfect squares surrounding it:

  • The square of 5 is 25.
  • The square of 6 is 36.

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

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

Now, we need to see if it is closer to 5 or 6.

Calculating \(5.5^2\):

\[ 5.5^2 = 30.25 \]

Since \(30.25\) is greater than \(28\), it confirms that \(\sqrt{28}\) is less than \(5.5\).

Calculating \(5.3^2\):

\[ 5.3^2 = 28.09 \]

Since \(28.09\) is greater than \(28\), it confirms that \(\sqrt{28}\) is less than \(5.3\).

Calculating \(5.2^2\):

\[ 5.2^2 = 27.04 \]

Since \(27.04\) is less than \(28\), it confirms that \(\sqrt{28}\) is greater than \(5.2\).

This means it is likely closer to \(5.3\).

Therefore, the correct answer is:

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