The order of a surd indicates the index of root to be extracted.
In \(\sqrt[n]{a}\), n is called the order of the surd and a is called the radicand.
For example: The order of the surd \(\sqrt[5]{z}\) is 5.
(i) A surd with 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 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).
(iv) A surd with index of root 4 is called a fourth order surd.
Example: \(\sqrt[4]{2}\), \(\sqrt[4]{3}\), \(\sqrt[4]{9}\), \(\sqrt[4]{17}\), \(\sqrt[4]{70}\), \(\sqrt[4]{a}\), \(\sqrt[4]{m}\), \(\sqrt[4]{x}\), \(\sqrt[4]{(x  1}\) are third order surd or cubic surd (since the indices of roots are 4).
(v) In general, a surd with index of root n is called a n\(^{th}\) order surd.
Example: \(\sqrt[n]{2}\), \(\sqrt[n]{3}\), \(\sqrt[n]{9}\), \(\sqrt[n]{17}\), \(\sqrt[n]{70}\), \(\sqrt[n]{a}\), \(\sqrt[n]{m}\), \(\sqrt[n]{x}\), \(\sqrt[n]{(x  1}\) are nth order surd (since the indices of roots are n).
Problem on finding the order of a surd:
Express ∛4 as a surd of order 12.
Solution:
Now, ∛4
= 4\(^{1/3}\)
= 4\(4^{\frac{1 × 4}{3 × 4}}\), [Since, we are to convert order 3 into 12, so we multiply both numerator and denominator of 1/3 by 4]
= 4\(^{4/12}\)
= \(\sqrt[12]{4^{4}}\)
= \(\sqrt[12]{256}\)
11 and 12 Grade Math
From Order of a Surd to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.