Topic Details (Notes format)

How to Simplify Radicals (Square Roots)

Subject: Mathematics

Book: Maths Mastery

Radical simplification often involves extracting perfect squares from under the radical sign. For √72, note 72 = 36 × 2, so √72 = √(36×2) = √36 × √2 = 6√2. More complex operations can include rationalizing denominators, e.g., 1 / √5 can be written as √5 / 5 by multiplying numerator and denominator by √5. Proficiency with radicals appears in geometry (Pythagorean distances), advanced algebra, and real-world measurements requiring root approximations. Frequent practice with factorization and rationalization ensures you handle square roots, cube roots, or higher-order radicals with confidence.

Practice Questions

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

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If the sum of three consecutive integers is 96, what are the integers?

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What is the square root of 121?

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

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