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]
