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

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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What is the LCM of 15 and 20?

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The probability of getting an even number when rolling a die is:

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