Using a number line, what whole number and rational number to the nearest half is 58−−√

Question

58
between?

Answer 1

To find the values that $\sqrt{58}$ lies between, we first need to approximate $\sqrt{58}$.

Calculating:

• Since $7^2=49$ and $8^2=64$, it follows that $7<\sqrt{58}<8$.

To narrow it down further, we can estimate:

• ${7.5}^2=56.25$ (which is less than 58)
• ${7.6}^2=57.76$ (which is also less than 58)
• ${7.7}^2=59.29$ (which is greater than 58)

From this, we can conclude:

$$7.6<\sqrt{58}<7.7$$

Next, we find the rational numbers to the nearest half. The closest halves to consider are:

• 7.5
• 8.0

Therefore, $\sqrt{58}$ is between $7.5$ and $7.7$, which means:

• The whole number $\sqrt{58}$ lies between is 7.
• The rational number to the nearest half is 7.5.

In summary, $\sqrt{58}$ is between the whole number 7 and the rational number 7.5.