Answer :

To evaluate the expression [tex]\(\frac{-5 \sqrt{73}}{212}\)[/tex], we can follow these steps:

1. Compute the numerator:
- The numerator of the expression is [tex]\(-5 \sqrt{73}\)[/tex].
- Taking the square root of [tex]\(73\)[/tex] gives approximately [tex]\(8.544\)[/tex].
- Now, multiply this value by [tex]\(-5\)[/tex]:
[tex]\[ -5 \cdot 8.544 \approx -42.720 \][/tex]
Hence, the numerator is approximately [tex]\(-42.720\)[/tex].

2. Identify the denominator:
- The denominator is [tex]\(212\)[/tex].

3. Divide the numerator by the denominator:
- We now divide [tex]\(-42.720\)[/tex] by [tex]\(212\)[/tex]:
[tex]\[ \frac{-42.720}{212} \approx -0.2015 \][/tex]
Thus, the result of the division is approximately [tex]\(-0.2015\)[/tex].

In summary, the steps led to the following intermediate values:
- Numerator: [tex]\(-42.720018726587654\)[/tex]
- Denominator: [tex]\(212\)[/tex]

By performing the division, we get the final result:
[tex]\[ \frac{-5 \sqrt{73}}{212} \approx -0.20150952229522479 \][/tex]

So, the approximate value of [tex]\(\frac{-5 \sqrt{73}}{212}\)[/tex] is [tex]\(-0.2015\)[/tex].