https://file.aiquickdraw.com/mathbot/file/1726432252452goqqkfoa.jpg

Let's break down and solve the two sections in the image.

### Section D: Simplifying Radicals (Square Roots)

1. \( \sqrt{49} = 7 \)
2. \( \sqrt{25} + \sqrt{16} = 5 + 4 = 9 \)
3. \( \sqrt{81} - \sqrt{9} = 9 - 3 = 6 \)
4. \( \sqrt{36} \times \sqrt{4} \times 2 = 6 \times 2 \times 2 = 24 \)
5. \( \sqrt{64} \div \sqrt{25} + \sqrt{9} = \frac{8}{5} + 3 = \frac{8}{5} + \frac{15}{5} = \frac{23}{5} \)
6. \( 2\sqrt{16} + 3\sqrt{9} - \sqrt{100} = 2(4) + 3(3) - 10 = 8 + 9 - 10 = 7 \)

### Section E: Simplifying Radicals with Variables (Including Odd Powers)

1. \( \sqrt{x^2} = x \)
2. \( \sqrt{16a^2} = 4a \)
3. \( 3\sqrt{4x^3} = 3 \times 2x^{3/2} = 6x^{3/2} \)
4. \( \sqrt{25b^2} + 2\sqrt{9c^3} = 5b + 6c^{3/2} \)
5. \( \sqrt{64a^3} + \sqrt{49b^2} = 8a^{3/2} + 7b \)
6. \( 2\sqrt{81x^3} - \sqrt{16y^5} = 18x^{3/2} - 4y^{5/2} \)
7. \( \sqrt{36m^3} + 3\sqrt{9n^5} = 6m^{3/2} + 9n^{5/2} \)
8. \( 2\sqrt{100p^4} + \sqrt{121q^3} - \sqrt{49r^5} = 20p^2 + 11q^{3/2} - 7r^{5/2} \)

Would you like further clarification or details on any of these steps?

Here are five related questions to consider:
1. How do you simplify radicals with odd exponents?
2. What are the rules for adding and subtracting radicals?
3. How do you deal with coefficients when simplifying square roots?
4. How can radicals be simplified when they include multiple variables?
5. What is the difference between simplifying an even power versus an odd power under a square root?

**Tip:** When simplifying radicals with variables, remember that even powers under the square root simplify completely, while odd powers leave a variable inside the radical.

Simplify the radicals and radical expressions with variables (including odd powers).

Learn how to simplify radicals with square roots and variables, including those with odd exponents. This guide covers step-by-step solutions for simplifying radical expressions, aimed at high school students (Grades 9-12).

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