whoever shall be worthy to answer this question is the brainliest. how to find order of a surd.give some examples.
Answers
Definitions of surds: A root of a positive real quantity is called a surd if its value cannot be exactly determined. It is a number that can’t be simplified to remove a square root (or cube root etc). For example, each of the quantities √3, ∛7, ∜19, (16)^2/5 etc. is a surd.
More Examples:
- √2 (square root of 2) can’t be simplified further so it is a surd
- √4 (square root of 4) CAN be simplified to 2, so it is NOT a surd
The order of a surd indicates the index of root to be extracted.
In a√n, n is called the order of the surd and a is called the radicand.
For example, The order of the surd 5√z is 5.
(i) A surd with an index of root 2 is called a second order surd or quadratic surd.
Example: √2, √5, √10, √a, √m, √x, √(x + 1) are second-order surd or quadratic surd (since the indices of roots are 2).
(ii) A surd with an index of root 3 is called a third order surd or cubic surd.
Example: ∛2, ∛5, ∛7, ∛15, ∛100, ∛a, ∛m, ∛x, ∛(x – 1) are third order surd or cubic surd (since the indices of roots are 3).