Sure, let's solve the given expression step by step:
The expression to be simplified is:
[tex]\[
\sqrt{\frac{-26 - (-17) - 24 - (-2) \cdot 6}{-3 - \frac{1}{2}}}
\][/tex]
Step 1: Simplify the numerator
1. Start with each individual term in the numerator:
- The first term is [tex]\(-26\)[/tex].
- The second term is [tex]\(-(-17)\)[/tex]. Simplify [tex]\(-(-17)\)[/tex] to [tex]\(17\)[/tex].
- The third term is [tex]\(-24\)[/tex].
- The fourth term involves multiplication: [tex]\(-(-2) \cdot 6\)[/tex]. Simplify [tex]\(-(-2)\)[/tex] to [tex]\(2\)[/tex], then calculate [tex]\(2 \cdot 6\)[/tex] which gives [tex]\(12\)[/tex].
2. Sum these simplified terms:
- Combine [tex]\(-26\)[/tex], [tex]\(17\)[/tex], [tex]\(-24\)[/tex], and [tex]\(12\)[/tex]:
[tex]\[
-26 + 17 - 24 + 12 = -31
\][/tex]
So, the numerator simplifies to [tex]\(-31\)[/tex].
Step 2: Simplify the denominator
1. Combine [tex]\(-3\)[/tex] and [tex]\(-\frac{1}{2}\)[/tex]:
[tex]\[
-3 - \frac{1}{2} = -3 - 0.5 = -3.5
\][/tex]
So, the denominator simplifies to [tex]\(-3.5\)[/tex].
Step 3: Evaluate the fraction
1. Compute the fraction:
[tex]\[
\frac{-31}{-3.5} = 8.857142857142858
\][/tex]
Step 4: Take the square root
1. Find the square root of the result:
[tex]\[
\sqrt{8.857142857142858} = 2.9760952365713798
\][/tex]
So, the final result is:
[tex]\[
\sqrt{\frac{-26-(-17)-24-(-2)(6)}{-3}-\frac{1}{2}} = 2.9760952365713798
\][/tex]
