Topic Details (Notes format)

How to Simplify Surds (Irrational Square Roots)

Subject: Mathematics

Book: Maths Mastery

“Surd” often refers to an irrational root that can’t be simplified to a rational number, like √2 or √7. We can simplify √18 to 3√2 by factoring out perfect squares. To add or subtract surds, they must share the same radicand: for instance, 2√3 + 3√3 = 5√3. Rationalizing denominators (like 1/√3 becoming √3/3) is key to presenting surd answers in standard form. Surd arithmetic underlies advanced algebra, geometry with exact distances, and calculations where approximations can degrade precision. Familiarity ensures you handle irrational values with exactness and clarity.

Practice Questions

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

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What is the sum of all odd numbers from 1 to 99?

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

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What is the sum of the first 10 positive even numbers?

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

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

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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

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