Question

using a number line, what whole number and rational number to the nearest half is \sqrt(58) between?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the whole number and rational number to the nearest half that \(\sqrt{58}\) is between, let's first simplify \(\sqrt{58}\):

\(\sqrt{58} \approx 7.61577\)

Now, let's identify the whole number and rational number to the nearest half that \(\sqrt{58}\) is between.

Whole number: The whole number that \(\sqrt{58}\) is between is 7.

Rational number to the nearest half: Since the number after the decimal point is closer to 0.5 than 1, the rational number to the nearest half that \(\sqrt{58}\) is between is 7.5.

So, \(\sqrt{58}\) is between 7 and 7.5 on the number line.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine the whole number and rational number to the nearest half that \(\sqrt{58}\) is between using a number line, we can start by estimating the square root.

Step 1: Estimate the square root of 58
- First, we can find two perfect square numbers that \(\sqrt{58}\) falls between. The perfect square numbers closest to 58 are 49 (\(7^2\)) and 64 (\(8^2\)).
- Since 58 is closer to 64 than 49, we can estimate \(\sqrt{58}\) to be slightly less than 8.

Therefore, we can say that \(\sqrt{58}\) is approximately \(<8\).

Step 2: Finding whole number and rational numbers to the nearest half
- To determine the whole number and rational number to the nearest half that \(\sqrt{58}\) is between, locate \(\sqrt{58}\) on a number line and identify the whole number and rational number values on either side of it.

| | | | | | | | |
5 6 6.5 7 7.5 8 8.5 9 9.5

- From our estimation in Step 1, we know that \(\sqrt{58}\) is less than 8. Therefore, \(\sqrt{58}\) lies between 7 and 8 on the number line.

Hence, the whole number to the nearest half that \(\sqrt{58}\) is between is 7, and the rational number to the nearest half that it is between is 7.5.

Answer 3

[AI-generated answer — Explain Bot]

To determine the whole number and rational number closest to √58 on a number line, we need to find the largest whole number and rational number that is less than √58 and the smallest whole number and rational number that is greater than √58.

To begin, let's calculate the value of √58. Taking the square root of 58, we find that √58 ≈ 7.61577.

Now, let's find the largest whole number that is less than √58. Since √58 is approximately 7.61577, the largest whole number less than √58 is 7.

Next, let's convert √58 to the nearest half. To find the nearest half, we check the closest multiples of 0.5. The multiples of 0.5 surrounding √58 are 7.5 and 8. Therefore, the nearest half to √58 is 7.5.

So, on the number line, √58 is between the whole number 7 and the rational number 7.5.