https://file.aiquickdraw.com/mathbot/file/1727225739402vmzveyd8.jpg

Let's go through the problems and simplify each one step by step:

1. \( \sqrt{98} = \sqrt{2 \times 49} = 7\sqrt{2} \)
2. \( \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \)
3. \( \sqrt{44} = \sqrt{4 \times 11} = 2\sqrt{11} \)
4. \( \sqrt{90a^3} = \sqrt{9 \times 10a^3} = 3a\sqrt{10a} \)
5. \( \sqrt{12a^2b^5} = \sqrt{4 \times 3a^2b^5} = 2ab^2\sqrt{3b} \)
6. \( \sqrt{a^3b^4c^2} = ab^2c\sqrt{a} \)
7. \( \sqrt{20a} = \sqrt{4 \times 5a} = 2\sqrt{5a} \)
8. \( \sqrt[3]{16} = \sqrt[3]{2^4} = 2\sqrt[3]{2} \)
9. \( \sqrt[3]{a^4b^6} = ab^2\sqrt[3]{a} \)
10. \( \sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2} \)
11. \( \sqrt[4]{a^2b^5} = a^{1/2}b^{5/4} \)
12. \( \sqrt[5]{a^{11}b^8c^{15}} = a^{11/5}b^{8/5}c^3 \)
13. \( \sqrt[3]{24a^6} = \sqrt[3]{8 \times 3a^6} = 2a^2\sqrt[3]{3} \)
14. \( \sqrt[99]{a^{103}} = a^{103/99} = a^{1 + 4/99} \)
15. \( \sqrt[3]{54} = \sqrt[3]{27 \times 2} = 3\sqrt[3]{2} \)
16. \( \sqrt{1000} = \sqrt{100 \times 10} = 10\sqrt{10} \)
17. \( \sqrt{100a^4} = 10a^2 \)
18. \( \sqrt[4]{32} = \sqrt[4]{2^5} = 2\sqrt[4]{2} \)

Would you like a deeper explanation of any of these steps?

### Related Questions:
1. How do you simplify a square root involving variables?
2. What are cube roots and how do they differ from square roots?
3. How do you simplify fractional exponents like \(a^{11/5}\)?
4. How do you express roots in terms of fractional exponents?
5. Can you break down higher-order roots (like 4th or 5th roots) the same way as square and cube roots?

**Tip:** Always factor numbers under the square or cube root as much as possible to simplify.

Simplify the list of square roots, cube roots, and higher-order roots.

This page explains how to simplify square roots, cube roots, and other higher-order radicals, including detailed examples like √98, √8, and cube roots of expressions involving variables. Learn the core concepts and formulas for simplifying these problems, suitable for Grades 9-12.

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