Problem 1: Simplify $\sqrt{5} \times \sqrt{20}$ using the property $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$.
Problem 2: Simplify $\sqrt{12} \times \sqrt{3}$.
Problem 3: Evaluate $(\sqrt{7})^2$ using the property $(\sqrt{a})^2 = a$.
Problem 4: Simplify $\sqrt{9} \times \sqrt{9}$.
Problem 5: Simplify $\frac{\sqrt{50}}{\sqrt{2}}$ using the property $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$.
Problem 6: Simplify $\frac{\sqrt{72}}{\sqrt{8}}$.
Problem 7: Simplify $\frac{5}{\sqrt{5}}$ using the property $\frac{a}{\sqrt{a}} = \sqrt{a}$.
Problem 8: Simplify $\frac{7}{\sqrt{7}}$.
Problem 9: Verify whether the following is true or false: $\sqrt{16} + \sqrt{9} = \sqrt{25}$.
Problem 10: Verify whether the following is true or false: $\sqrt{36} – \sqrt{16} = \sqrt{20}$
1. Simplify $\sqrt{5} \times \sqrt{20}$ using the property $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$
Step: Multiply the numbers inside the square roots: $\sqrt{5 \times 20} = \sqrt{100}$.
Final Answer: Since $10 \times 10 = 100$, the result is 10.
2. Simplify $\sqrt{12} \times \sqrt{3}$
Step: Use the multiplication property: $\sqrt{12 \times 3} = \sqrt{36}$.
Final Answer: Since $6 \times 6 = 36$, the result is 6.
3. Evaluate $(\sqrt{7})^2$ using $(\sqrt{a})^2 = a$
Step: Squaring a square root cancels out the radical sign.
Final Answer: The result is 7.
4. Simplify $\sqrt{9} \times \sqrt{9}$
Step: This is the same as $(\sqrt{9})^2$. You can also solve it as $3 \times 3$.
Final Answer: The result is 9.
5. Simplify $\frac{\sqrt{50}}{\sqrt{2}}$ using $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$
Step: Combine the division under one root: $\sqrt{\frac{50}{2}} = \sqrt{25}$.
Final Answer: Since $5 \times 5 = 25$, the result is 5.
6. Simplify $\frac{\sqrt{72}}{\sqrt{8}}$
Step: Divide the radicands: $\sqrt{\frac{72}{8}} = \sqrt{9}$.
Final Answer: The result is 3.
7. Simplify $\frac{5}{\sqrt{5}}$ using $\frac{a}{\sqrt{a}} = \sqrt{a}$
Step: When a number is divided by its own square root, the result is the square root of that number.
Final Answer: The result is $\sqrt{5}$.
8. Simplify $\frac{7}{\sqrt{7}}$
Step: Apply the same property as Problem 7.
Final Answer: The result is $\sqrt{7}$.
9. Verify whether $\sqrt{16} + \sqrt{9} = \sqrt{25}$ is true or false
Left Side: $\sqrt{16} + \sqrt{9} = 4 + 3 = 7$.
Right Side: $\sqrt{25} = 5$.
Explanation: $7 \neq 5$. You cannot simply add the numbers inside square roots.
Final Answer: False.
10. Verify whether $\sqrt{36} – \sqrt{16} = \sqrt{20}$ is true or false
Left Side: $\sqrt{36} – \sqrt{16} = 6 – 4 = 2$.
Right Side: $\sqrt{20}$ is approximately $4.47$.
Explanation: $2 \neq \sqrt{20}$. Similar to addition, you cannot subtract numbers inside square roots.
Final Answer: False.