Surds

A surd is an irrational root that cannot be written as an exact decimal. In this topic you will learn how to simplify surds, use the basic rules for multiplying and dividing, add and subtract like surds, and rationalise the denominator.

  • Simplifying surds
  • Multiplying and dividing surds
  • Adding and subtracting like surds
  • Rationalising the denominator

Lessons for Surds

What is a Surd and Simplifying

What is a surd?A surd is a root of a number that is irrational. Examples: √2, √3, √5.√4 = 2 …

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Multiplying and Dividing Surds

RulesMultiplying: √a × √b = √(ab)Dividing: √a ÷ √b = √(a/b)Examples√2 × √8 = √16 = 43√5 × 2√2 = …

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Adding and Subtracting Surds

Like surdsYou can only add or subtract 'like' surds, just like like terms in algebra.2√3 + 5√3 = 7√36√2 - …

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Rationalising the Denominator

Why rationalise?It is standard to remove surds from the bottom of a fraction.Type 1: Single surdMultiply top and bottom by …

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Exercises for Surds

Simplify the surd

Simplify fully:√8√18√27√45√48√200

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Multiply and divide

Simplify:√3 × √122√5 × 3√2√6 × √15√50 ÷ √28√20 ÷ 4√5(√6)2

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Add and subtract

Simplify:3√5 + 2√57√3 - 4√3√12 + √27√45 - √202√8 + √18 - √25√6 - 2√24 + √54

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Rationalise the denominator

Rationalise and simplify:1/√53/√2√6/√31/(3+√2)4/(5-√3)(√5+1)/(√5-1)

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