Sure! Let's evaluate the given expression step-by-step:
The given expression is:
[tex]\[ \frac{\sqrt{-8 + 3 \cdot 8} + \left| -10 - 28 \right|}{-119 - (-5)^3} \][/tex]
Step 1: Simplify inside the square root:
First, look inside the square root:
[tex]\[ -8 + 3 \cdot 8 \][/tex]
Calculate [tex]\( 3 \cdot 8 \)[/tex]:
[tex]\[ 3 \cdot 8 = 24 \][/tex]
Then,
[tex]\[ -8 + 24 = 16 \][/tex]
So the expression inside the square root simplifies to 16. Next, calculate the square root:
[tex]\[ \sqrt{16} = 4 \][/tex]
Step 2: Simplify inside the absolute value:
Now, look inside the absolute value:
[tex]\[ -10 - 28 \][/tex]
Subtract [tex]\( 28 \)[/tex] from [tex]\( -10 \)[/tex]:
[tex]\[ -10 - 28 = -38 \][/tex]
The absolute value of [tex]\(-38\)[/tex] is:
[tex]\[ \left| -38 \right| = 38 \][/tex]
Step 3: Calculate the denominator:
Next, simplify the denominator:
[tex]\[ -119 - (-5)^3 \][/tex]
First, calculate [tex]\((-5)^3\)[/tex]:
[tex]\[ (-5)^3 = -125 \][/tex]
Then, substitute this value into the denominator:
[tex]\[ -119 - (-125) \][/tex]
This simplifies to:
[tex]\[ -119 + 125 = 6 \][/tex]
Step 4: Combine the results:
Now we have all the parts:
- Square root result: 4
- Absolute value result: 38
- Denominator: 6
Combine the results into the original expression:
[tex]\[ \frac{\sqrt{16} + \left| -38 \right|}{-119 - (-125)} \][/tex]
Substitute the values:
[tex]\[ \frac{4 + 38}{6} \][/tex]
Step 5: Solve the final expression:
[tex]\[ \frac{4 + 38}{6} = \frac{42}{6} \][/tex]
[tex]\[ \frac{42}{6} = 7 \][/tex]
Hence, the value of the expression is:
[tex]\[ 7 \][/tex]
