Surds
Rational and Irrational
● Some numbers are irrational - cannot be expressed as fractions as
decimals go on forever without pattern
● Square root of number that isn’t perfect square is also irrational
● However this is partly rational as you can write it as the square root of a
rational number
● These numbers are called surds
Simplifying Surds
● Take the number inside the square root function and write it in terms of its
prime factors
● Find any prime factors that are raised to a power greater than one
● Take those factors out of the square root
Example
S implif y √12
√12 = √22 × 3
= √22 × √3
= 2√3
Adding and Subtracting Surds
● Treat like algebra
● Simplify surds
● Collect like terms
● Like terms are any rational numbers or any surds involving the same
number
Example
E valuate √32 − √18
√32 − √18 = √25 − √2 × 32
= 4√2 − 3√2
= √2
Multiplying Surds
● Multiply surds as you would multiply any numbers
● Simplify surds
● Multiply the numbers within the square roots
● Simplify final answer
Rational and Irrational
● Some numbers are irrational - cannot be expressed as fractions as
decimals go on forever without pattern
● Square root of number that isn’t perfect square is also irrational
● However this is partly rational as you can write it as the square root of a
rational number
● These numbers are called surds
Simplifying Surds
● Take the number inside the square root function and write it in terms of its
prime factors
● Find any prime factors that are raised to a power greater than one
● Take those factors out of the square root
Example
S implif y √12
√12 = √22 × 3
= √22 × √3
= 2√3
Adding and Subtracting Surds
● Treat like algebra
● Simplify surds
● Collect like terms
● Like terms are any rational numbers or any surds involving the same
number
Example
E valuate √32 − √18
√32 − √18 = √25 − √2 × 32
= 4√2 − 3√2
= √2
Multiplying Surds
● Multiply surds as you would multiply any numbers
● Simplify surds
● Multiply the numbers within the square roots
● Simplify final answer
