Using a number line, what whole number and rational number to the nearest half is square root of 58 between? (1 point)

Answer 1

To find the square root of 58, we note that it lies between two perfect squares:

• $7^2=49$
• $8^2=64$

Therefore,

$$7<\sqrt{58}<8$$

Next, we can determine the approximate value of $\sqrt{58}$. Since $58$ is closer to $64$ than to $49$, we can estimate that $\sqrt{58}$ is closer to $8$.

Calculating the square roots of numbers around 58 gives:

• ${7.5}^2=56.25$
• ${7.6}^2=57.76$
• ${7.7}^2=59.29$

Since $58$ is between ${7.6}^2$ and ${7.7}^2$, we can conclude that:

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

Thus, when rounding $\sqrt{58}$ to the nearest half:

• $7.5$ rounds up to $8$,
• $7.6$ rounds down to $7.5$,
• $7.7$ rounds down to $7.5$.

Therefore, the value of $\sqrt{58}$ when rounded to the nearest half is approximately $7.5$.

To summarize:

• The whole number $\sqrt{58}$ is between is $7$ and $8$.
• The rational number rounded to the nearest half is $7.5$.