Topic Details (Notes format)

How to Identify and Use Perfect Cubes

Subject: Mathematics

Book: Maths Mastery

A perfect cube is an integer that is the cube of another integer, such as 27 = 3³ or 64 = 4³. Spotting these efficiently helps with factoring polynomials (like x³ – 8) or simplifying cube roots. Perfect cubes appear in 3D volume calculations, for instance, a 5×5×5 cube has a volume of 125. Understanding these patterns (1, 8, 27, 64, 125, ...) can streamline computations and deepen your exploration of algebraic identities like a³ ± b³. Whether comparing volumes or factoring expressions, perfect cubes are a potent tool in advanced math and practical tasks.

Practice Questions

What is the remainder when 5^100 is divided by 3?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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If x^2 + 4x + 4 = 0, what is the value of x?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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If the average of five consecutive odd numbers is 25, what is the largest number?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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If x - y = 5 and x + y = 15, what is the value of x?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If 3x = 81, what is the value of x?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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