Here are the step-by-step solutions for the provided problems:

13. $\sqrt{4} - \sqrt{121}$

$\sqrt{4} = 2, \quad \sqrt{121} = 11$

$\sqrt{4} - \sqrt{121} = 2 - 11 = -9$

14. $\sqrt{33} + 3$

$\sqrt{33} \approx 5.744, \quad \text{so } \sqrt{33} + 3 = 5.744 + 3 \approx 8.744$

15. $\sqrt{91} - 27$

$\sqrt{91} \approx 9.533, \quad \text{so } \sqrt{91} - 27 = 9.533 - 27 \approx -17.467$

16. $\sqrt{49} + \sqrt{100}$

$\sqrt{49} = 7, \quad \sqrt{100} = 10$

$\sqrt{49} + \sqrt{100} = 7 + 10 = 17$

17. $\sqrt{49} + 0$

$\sqrt{49} = 7, \quad \text{so } \sqrt{49} + 0 = 7$

18. $(\sqrt{100})^2$

$\sqrt{100} = 10, \quad (\sqrt{100})^2 = 10^2 = 100$

Final Answers:

1. $-9$
2. $8.744$ (approximate)
3. $-17.467$ (approximate)
4. $17$
5. $7$
6. $100$

Do you want further details or clarification on any of these steps?

Follow-Up Questions:

1. What is the process for simplifying square roots involving approximate values?
2. How does the property $(\sqrt{x})^2 = x$ help simplify expressions?
3. Why is $\sqrt{121}$ an exact number but $\sqrt{91}$ is not?
4. Can $\sqrt{33} + 3$ be simplified further without approximations?
5. How are properties of radicals used when solving equations?

Tip:

When working with square roots, remember to check if the number is a perfect square to avoid unnecessary approximations.