Question
Complete the following statement. Use the integers that are closest to the number in the middle. \( \square<\sqrt{77}<\square \) Submit
Ask by Kelley Clark.
Mar 21,2025 15:03
UpStudy AI Solution
Tutor-Verified Answer
Answer
\[ 8 < \sqrt{77} < 9 \]
Solution
To complete the statement \( \square < \sqrt{77} < \square \), we first need to find the integer values that are closest to \( \sqrt{77} \).
1. Calculate \( \sqrt{77} \).
2. Identify the integers that are just below and just above this value.
Let's start by calculating \( \sqrt{77} \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{77}{1}\)
- step1: Divide the terms:
\(77\)
Calculate or simplify the expression \( \sqrt(77) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{77}\)
The approximate value of \( \sqrt{77} \) is \( \approx 8.774964 \).
Now, we can identify the integers closest to this value:
- The integer just below \( 8.774964 \) is \( 8 \).
- The integer just above \( 8.774964 \) is \( 9 \).
Thus, we can complete the statement as follows:
\[ 8 < \sqrt{77} < 9 \]
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Simplify this solution Beyond the Answer
To find the integers closest to \( \sqrt{77} \), we can calculate it approximately. Since \( 8^2 = 64 \) and \( 9^2 = 81 \), we see that \( 8 < \sqrt{77} < 9 \). Thus, we can complete the statement:
\( 8 < \sqrt{77} < 9 \)
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