Sure! Let's solve the given expression step-by-step:
Given expression:
[tex]\[ = \frac{1.666 - 0.418}{\sqrt{0.17508 \left[\frac{1}{5} + \frac{1}{5}\right]}} \][/tex]
Step 1: Calculate the numerator
First, perform the subtraction in the numerator:
[tex]\[ 1.666 - 0.418 = 1.248 \][/tex]
Step 2: Simplify the expression inside the square root (denominator)
Inside the square root, we first need to simplify [tex]\(\frac{1}{5} + \frac{1}{5}\)[/tex]:
[tex]\[ \frac{1}{5} + \frac{1}{5} = \frac{1+1}{5} = \frac{2}{5} \][/tex]
Then, we multiply this result by 0.17508:
[tex]\[ 0.17508 \times \frac{2}{5} = 0.17508 \times 0.4 = 0.070032 \][/tex]
Step 3: Take the square root
Now, take the square root of the result obtained in step 2:
[tex]\[ \sqrt{0.070032} \approx 0.26463559851236945 \][/tex]
Step 4: Divide the numerator by the denominator
Finally, divide the numerator by the square root calculated in step 3:
[tex]\[ \frac{1.248}{0.26463559851236945} \approx 4.71591882201618 \][/tex]
Conclusion:
So, the value of the given expression is approximately [tex]\(4.71591882201618\)[/tex].
