Simplifying Surds

Surds & Exact Values 

What is a surd? 

• A surd represents the square root of a non-square integer. Employing surds allows you to maintain answers in exact form, such as
• Using surds lets you leave answers in exact form, for instance, instead of
  

How do I calculate with surds?

• Multiplication of Surds
  • When multiplying numbers under square roots, multiply them together.
  • For example,
• Division of Surds
  • When dividing numbers under square roots, you can divide them.
  • For instance,
• Factorising Surds
  • To factorise numbers under square roots, express them as a product of square roots.
  • For example,
• Adding or Subtracting Surds
  • Adding or subtracting surds is akin to operating with algebraic variables.
  • Remember, you can only add or subtract similar surds, i.e., those with the same root.
    • For instance,
  • Be cautious when dealing with surds - you cannot directly add or subtract numbers under square roots.
    • Think about
    • It is not equal to

Simplifying Surds

How to Simplify Surds?

• To simplify a surd, identify and extract any square factors present and take their square root. Find the largest square number that divides the number you are simplifying.
• For eg:

• You can collect like terms with surds like you do with letters in algebra
• Understanding how to simplify surds can help reduce expressions and collect like terms
  
• An important skill is multiplying double brackets containing surds
  • This can be done in the same way as multiplying out double brackets algebraically and simplifying
  • The property  can be used to simplify the expression, once expanded