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 2x = 16, what is the value of x?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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What is the length of the diagonal of a square with a side length of 7 cm?

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What is the LCM of 15 and 20?

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If the radius of a circle is 7 cm, what is its circumference?

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What is the sum of the first 10 positive even numbers?

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

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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What is the cube root of 729?

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