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

If a number is divisible by 9, it is also divisible by which of the following?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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