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

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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If 2x = 16, what is the value of x?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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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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What is the area of an equilateral triangle with side length 10 cm?

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What is the square root of 144?

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