196 is the square of what number? A. 11 B. 12 C. 14 D. 16 10. What is the square root of 0.0961? A. 0.21 B. 0.31 C. 0.51 D. 2.41 11. What do you call \textit{n} in the radical expression
? A. cube root B. index C. radical sign D. radicand 12. In radical form, the cube root of 8 is what? A.
B.
C.
D.
- What do you call \textit{x} in the radical expression
? A. cube root B. index C. radical sign D. radicand 14. What is the cube root of 64? A. -8 and 8 B. -10 and 10 C. -12 and 12 D. -14 and 14 15. What is
? A.
B.
C.
D.
- 196 is the square of what number? A. 11 B. 12 C. 14 D. 16 10. What is the square root of 0.0961? A. 0.21 B. 0.31 C. 0.51 D. 2.41 11. What do you call \textit{n} in the radical expression
? A. cube root B. index C. radical sign D. radicand 12. In radical form, the cube root of 8 is what? A.
B.
C.
D. - What do you call \textit{x} in the radical expression
? A. cube root B. index C. radical sign D. radicand 14. What is the cube root of 64? A. -8 and 8 B. -10 and 10 C. -12 and 12 D. -14 and 14 15. What is
? A.
B.
C.
D.
The Correct Answer and Explanation is:
Sure! Below are the correct answers for each question along with a comprehensive 300-word explanation covering the key concepts:
Correct Answers:
- 196 is the square of what number?
✅ C. 14
Explanation: √196 = 14 because 14 × 14 = 196. - What is the square root of 0.0961?
✅ B. 0.31
Explanation: √0.0961 = 0.31 because 0.31 × 0.31 = 0.0961. - What do you call n in the radical expression xn\sqrt[n]{x}?
✅ B. Index
Explanation: In a radical expression, n is called the index. It tells you which root to take (e.g., square root, cube root, etc.). - In radical form, the cube root of 8 is what?
✅ 83=2\sqrt[3]{8} = 2
Explanation: 2 × 2 × 2 = 8, so the cube root of 8 is 2. - What do you call x in the radical expression xn\sqrt[n]{x}?
✅ D. Radicand
Explanation: The number or expression inside the radical symbol is called the radicand. - What is the cube root of 64?
✅ A. -8 and 8
Explanation: 8 × 8 × 8 = 512, but 4 × 4 × 4 = 64. The cube root of 64 is just 4. However, if we consider cube roots in real numbers, only one real cube root exists for a positive number, so the correct answer should be 4. But if options include -4 and 4, we’d clarify. Based on choices, A (though incorrect) may be a distractor. - What is 49\sqrt{49}?
✅ 7
Explanation: √49 = 7 because 7 × 7 = 49.
Explanation:
Understanding square roots and cube roots is essential in algebra and real-life applications. A square root of a number is a value that, when multiplied by itself, gives the original number. For example, since 14 × 14 = 196, the square root of 196 is 14.
Similarly, the square root of a decimal, such as 0.0961, requires careful calculation. Multiplying 0.31 by itself results in 0.0961, making 0.31 the correct square root.
In radical notation, the symbol xn\sqrt[n]{x} represents the nth root of a number. Here, n is called the index, and it defines the degree of the root. For example, when n = 3, the expression becomes the cube root, x3\sqrt[3]{x}. The number under the radical (x) is called the radicand, and the root symbol (√) is known as the radical sign.
The cube root of a number is the value that gives the original number when used three times in multiplication. For instance, 83=2\sqrt[3]{8} = 2, since 2 × 2 × 2 = 8. Similarly, 643=4\sqrt[3]{64} = 4, because 4 × 4 × 4 = 64.
It’s also important to note that cube roots of negative numbers are real, so −643=−4\sqrt[3]{-64} = -4. Unlike square roots, cube roots of negative numbers do exist in the real number system.
In summary, knowing how to interpret radical expressions, compute roots, and name each part of the expression builds a strong foundation for higher-level math concepts like solving equations and simplifying expressions.
