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Cube and Cube Roots
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Flashcards: Cube and Cube Roots Flashcard | Improve Your Calculations: Vedic Maths (English) - Class 6
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1. What is a cube in mathematical terms?
Ans. In mathematics, a cube is a three-dimensional geometric figure with six equal square faces. The volume of a cube can be calculated using the formula \( V = a^3 \), where \( a \) is the length of one side of the cube.
2. How do you calculate the cube of a number?
Ans. To calculate the cube of a number, you multiply the number by itself twice. For example, to find the cube of 3, you would calculate \( 3 \times 3 \times 3 = 27 \).
3. What is a cube root, and how is it represented?
Ans. A cube root is a number that, when multiplied by itself three times, gives the original number. It is represented by the radical symbol with a small three, written as \( \sqrt[3]{x} \). For example, the cube root of 27 is 3, because \( 3 \times 3 \times 3 = 27 \).
4. Can you give examples of perfect cubes and their cube roots?
Ans. Yes! Some examples of perfect cubes include: - \( 1^3 = 1 \), cube root is 1. - \( 2^3 = 8 \), cube root is 2. - \( 3^3 = 27 \), cube root is 3. - \( 4^3 = 64 \), cube root is 4.
5. Why are cube roots important in mathematics?
Ans. Cube roots are important in mathematics because they help in solving equations involving cubic functions, understanding volume calculations in geometry, and in various applications in science and engineering where three-dimensional space is involved.
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