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

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

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If the probability of an event is 1/4, what is the probability of its complement?

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

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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If sin(A) = 1/2 and A is acute, what is the value of A?

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If 5x - 2 = 13, what is the value of x?

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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