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```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}
```

Sagot :

GinnyAnswer
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]
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