Question

Use a calculator to solve the equation below. Use pencil and paper. Before computing​ anything, write down two perfect squares you​ know, one that is less than the given number and one that is greater than the given number. Then write down their square roots as two numbers you know k must be between.
ksquaredequals107
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Part 1
kalmost equals
  
enter your response here
​(Round to the nearest tenth as needed. Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \( k^2 = 107 \), we can start by identifying two perfect squares: one less than 107 and one greater than 107.

1. **Perfect squares**:
- 10² = 100 (this is less than 107)
- 11² = 121 (this is greater than 107)

2. **Square roots**:
- The square root of 100 is 10.
- The square root of 121 is 11.

This means that \( k \) must be between 10 and 11, or:

\[
10 < k < 11
\]

Now, calculate the exact value of \( k \) by taking the square root of 107:

\[
k = \sqrt{107} \approx 10.344
\]

Finally, rounding to the nearest tenth, we have:

\[
k \approx 10.3
\]

So, you would write:

**Answer:**
\( k \approx 10.3 \)