Using a number line, what whole number and rational number to the nearest half is √96 between?

Question

A. 9 and 9.5
B. 9.5 and 10
C. 10 and 10.5
D. 10.5 and 11

Answer 1

To find between which whole numbers \( \sqrt{96} \) lies, we first need to calculate \( \sqrt{96} \).

We can simplify \( \sqrt{96} \): \[ \sqrt{96} = \sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6} \]

Next, we can find the approximate value of \( \sqrt{6} \). Since we know that \( 2.4^2 = 5.76 \) and \( 2.5^2 = 6.25 \), we can estimate that \( \sqrt{6} \) is slightly greater than \( 2.4 \) but less than \( 2.5 \).

For better accuracy, we can use a calculator to find: \[ \sqrt{6} \approx 2.449 \]

Now we multiply by 4: \[ \sqrt{96} \approx 4 \times 2.449 \approx 9.796 \]

Next, we determine where \( 9.796 \) lies on the number line in relation to whole and rational numbers. The nearest half values surrounding \( 9.796 \) are \( 9.5 \) and \( 10 \).

From this calculation, \( \sqrt{96} \) is between: \[ 9.5 \quad \text{and} \quad 10 \]

Thus, the answer is: B. 9.5 and 10

Answer 2

put that in simplier/normal ppl terms pls

Answer 3

Sure! Let's break it down step by step:

1. Find \( \sqrt{96} \): We want to figure out the square root of 96.

2. Estimate the value:

   • We know that the square root of 81 is 9 (since \( 9 \times 9 = 81 \)) and the square root of 100 is 10 (since \( 10 \times 10 = 100 \)).
   • This tells us that \( \sqrt{96} \) is between 9 and 10.

3. Get a closer estimate:

   • We can find that \( \sqrt{96} \) is actually about 9.8.

4. Compare to whole numbers:

   • The two closest numbers are 9.5 and 10. Since 9.8 is greater than 9.5 but less than 10, we can see that:

So, \( \sqrt{96} \) is between 9.5 and 10. The answer is B: 9.5 and 10.