Topic Details (Notes format)

How to Identify and Use Perfect Squares

Subject: Mathematics

Book: Maths Mastery

A perfect square is an integer that is the square of another integer, like 16 = 4² or 81 = 9². Recognizing perfect squares is helpful in radical simplifications, factoring, or analyzing quadratic equations. Quick identification is also handy in mental math, especially for approximate square roots. Perfect squares form patterns (1, 4, 9, 16, 25, 36, ...), widely applied in geometry (areas of squares), optimization problems, and numerous real-world calculations. Familiarity with them accelerates solutions to equations or shapes your ability to estimate square roots on the fly.

Practice Questions

If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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A cube has a side length of 4 cm. What is its volume?

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What is the area of a circle with a diameter of 14 cm?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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

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The LCM of 12 and 15 is:

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

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If x^2 - 5x + 6 = 0, what are the roots?

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What is the sum of all even numbers between 1 and 100?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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