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

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

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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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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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The probability of rolling a sum of 7 with two dice is:

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What is the sum of the first 50 positive integers?

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

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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

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