Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point) Responses between 7.5 and 8 between 7.5 and 8 between 7 and 7.5 between 7 and 7.5 between 8 and 8.5 between 8 and 8.5 between 8.5 and 9

Answer 1

To determine where \( \sqrt{58} \) is located on a number line, we can first find its approximate value.

Calculating \( \sqrt{58} \):

• We know that \( 7^2 = 49 \) and \( 8^2 = 64 \).
• Therefore, \( \sqrt{58} \) is between 7 and 8.

To get a more precise approximation, we can do some calculations:

• Let's find the average of 7 and 8: \[ 7.5^2 = 56.25 \] (which is less than 58)

  \[ 7.6^2 = 57.76 \] (still less than 58)

  \[ 7.7^2 = 59.29 \] (which is greater than 58)

From this, we can determine that \( \sqrt{58} \) is between 7.6 and 7.7, hence it is still less than 8.

So, \( \sqrt{58} \) is approximately 7.6, which places it between 7.5 and 8.

Therefore, the whole number portion is 7 and the rational number to the nearest half is 7.5.

So the correct range would be: between 7.5 and 8.