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].
