To solve the expression [tex]\(-12 + \sqrt{32}\)[/tex] and approximate it to the nearest tenth, let's break it down step-by-step:
1. Find the square root of 32:
The value of [tex]\(\sqrt{32}\)[/tex] is approximately 5.656854249492381.
2. Add the square root value to -12:
Next, we perform the addition:
[tex]\[
-12 + 5.656854249492381 = -6.343145750507619
\][/tex]
3. Round the result to the nearest tenth:
To round [tex]\(-6.343145750507619\)[/tex] to the nearest tenth, we look at the digit in the hundredths place, which is 4. Since 4 is less than 5, we round down. This results in:
[tex]\[
-6.3
\][/tex]
Thus, the approximate value of [tex]\(-12 + \sqrt{32}\)[/tex] to the nearest tenth is [tex]\(\boxed{-6.3}\)[/tex].
