```latex
\begin{array}{rlrl}
36 + (-58) & = & & (45)(-8) = \\
-39 + (-51) & = & 40 & (-2)(15) = \\
43 - (-12) & = & 35 & & \frac{-36}{18} = \\
-59 - (-27) & = & 32 &
\end{array}

\begin{array}{l}
\frac{54}{-27} = \\
\frac{-144}{-12} =
\end{array}

Calcula la raíz cuadrada de los siguientes números:

\sqrt{361} \quad \sqrt{729} \quad \sqrt{7569}
```

Of course! Let's proceed with a detailed step-by-step solution for each calculation mentioned in the question:

1. Calculations

1.1. [tex]$ 36 + (-58) $[/tex]
- When we add 36 and -58, we subtract 58 from 36: [tex]$ 36 - 58 = -22 $[/tex].

1.2. [tex]$ 45 \times (-8) $[/tex]
- Multiplying 45 by -8 gives us [tex]$ 45 \times -8 = -360 $[/tex].

1.3. [tex]$ -39 + (-51) $[/tex]
- Adding two negative numbers, -39 and -51, gives us a larger negative number: [tex]$ -39 + (-51) = -90 $[/tex].

1.4. [tex]$ -2 \times 15 $[/tex]
- Multiplying -2 by 15 results in [tex]$ -2 \times 15 = -30 $[/tex].

1.5. [tex]$ 43 - (-12) $[/tex]
- Subtracting a negative number is the same as adding the absolute value of that number: [tex]$ 43 - (-12) = 43 + 12 = 55 $[/tex].

1.6. [tex]$ \frac{-36}{18} $[/tex]
- Dividing -36 by 18 results in [tex]$ \frac{-36}{18} = -2.0 $[/tex].

1.7. [tex]$ -59 - (-27) $[/tex]
- Similar to 1.5, subtracting a negative number is like adding it: [tex]$ -59 - (-27) = -59 + 27 = -32 $[/tex].

1.8. [tex]$ \frac{54}{-27} $[/tex]
- Dividing 54 by -27 yields [tex]$ \frac{54}{-27} = -2.0 $[/tex].

1.9. [tex]$ \frac{-144}{-12} $[/tex]
- Dividing a negative number by another negative number results in a positive number: [tex]$ \frac{-144}{-12} = 12.0 $[/tex].

2. Square Roots

2.1. [tex]$ \sqrt{361} $[/tex]
- Taking the square root of 361 gives us [tex]$ 19.0 $[/tex].

2.2. [tex]$ \sqrt{729} $[/tex]
- Taking the square root of 729 results in [tex]$ 27.0 $[/tex].

2.3. [tex]$ \sqrt{7569} $[/tex]
- Taking the square root of 7569 yields [tex]$ 87.0 $[/tex].

So, summarizing all the results, we get:

- [tex]$ 36 + (-58) = -22 $[/tex]
- [tex]$ 45 \times (-8) = -360 $[/tex]
- [tex]$ -39 + (-51) = -90 $[/tex]
- [tex]$ -2 \times 15 = -30 $[/tex]
- [tex]$ 43 - (-12) = 55 $[/tex]
- [tex]$ \frac{-36}{18} = -2.0 $[/tex]
- [tex]$ -59 - (-27) = -32 $[/tex]
- [tex]$ \frac{54}{-27} = -2.0 $[/tex]
- [tex]$ \frac{-144}{-12} = 12.0 $[/tex]
- [tex]$ \sqrt{361} = 19.0 $[/tex]
- [tex]$ \sqrt{729} = 27.0 $[/tex]
- [tex]$ \sqrt{7569} = 87.0 $[/tex]