The order of surd is the index of it’s root.
√5 √7 √11 are examples of surds of second order.
∛5 ∛7 ∛11 are examples of surds of order three.
Example
Example
Arrange the following surds in ascending order.
solution
The solution will involve changing the surds so that they can be of the same order. Then we can compare their values from inside the root.
Like and unlike surds
Surds are alike if they have the same irrational factor, otherwise they are unlike surds.
Example
Solution
27 and 12 can be simplified such that they become a product of both rational and irrational numbers.
like 27 is a product of 9 and 3. and when we get the squareroot of 9, we gat a rational number 3.
similarly, 12 is a product of 4 and 3 and when we write 4 under square-root, it results to 2 which is rational. now both 12 and 27 and 1/3 when simplified will have the same irrational number as shown below
To simplify expressions involving surds, we simply add or subtract coefficient of irrational factors that are alike. thus
