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 a:b = 5:7 and b:c = 6:11, what is a:c?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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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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If x^2 + 4x + 4 = 0, 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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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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What is the LCM of 15 and 20?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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