Surds (Simplify & Rationalising)

Download: Surds – Revision

What are surds?

Surds can be used to give exact answers to calculations by leaving some numbers as square roots.

The square has a side length of √10 cm. You cannot write √10 exactly as a decimal number. Therefore, this is called a surd.

Golden Rules for Surds: (These rules need to be remembered for your exam)

√ab = √a x √b (Example: √12 = √4 x √3 = 2√3)

√ ᵃ/b = √ᵃ / √b (Example: √³/₂₅ = √³/√₂₅ = √³ / ₅)

(√a)² = √a x √a (Example (√2)² = √2 x √2 = 2)

(√a + √b) (√a – √b) = a – b (Example (√4+ √2) (√4 – √2) = 4 – 2 = 2)

Rationalising the Denominator:

This removes any surd in the denominator and makes it a whole number. You can do this by multiplying the top and bottom of the fraction by the surd part.

In order to figure out what to multiply the top and bottom by, look at the denominator of the original fraction. Swap the plus for a minus or swap a minus for a plus.

Worked Examples:

 

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