Subscribe to our YouTube channel for the latest videos, updates, and tips.


Order of a Surd

The order of a surd indicates the index of root to be extracted.

In na, n is called the order of the surd and a is called the radicand.

For example: The order of the surd 5z is 5.

(i) A surd with index of root 2 is called a second order surd or quadratic surd.

The surds which have the indices of root 2 are called as second order surds or quadratic surds. For example√2, √3, √5, √7, √x are the surds of order 2.

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.

If x is a positive integer with nth root, then  is a surd of nth order when the value of  is irrational. In  expression n is the order of surd and x is called as radicand. For example  is surd of order 3.

The surds which have the indices of cube roots are called as third order surds or cubic surds. For example ∛2, ∛3, ∛10, ∛17, ∛x are the surds of order 3 or cubic surds.

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).


(iii) A surd with index of root 4 is called a fourth order surd.

The surds which have the indices of four roots are called as forth order surds or bi-quadratic surds.

For example ∜2, ∜4, ∜9, ∜20, ∜x are the surds of order 4.

Example: 42, 43, 49, 417, 470, 4a, 4m, 4x, 4x1 are third order surd or cubic surd (since the indices of roots are 4).


(iv) In general, a surd with index of root n is called a nth order surd.

Similarly the surds which have the indices of n roots are nth order surds. n2, n17, n19, nx are the surds of order n.

Example: n2, n3, n9, n17, n70, na, nm, nx, nx1 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

= 41/3

= 41×43×4, [Since, we are to convert order 3 into 12, so we multiply both numerator and denominator of 1/3 by 4]

= 44/12

= 1244

= 12256


Problems on finding the order of surds:

1. Express √2 as a surd of order 6.

Solution:

√2 = 21/2

     = 21×32×3

     = 236

     = 81/6

     = 68

So 68 is a surd of order 6.


2. Express ∛3 as a surd of order 9.

Solution:

∛3 = 31/3

     = 31×33×3

     = 339

     = 271/9

     = 927

So 927 is a surd of order 9.


3. Simplify the surd  ∜25 to a quadratic surd.

Solution:

 ∜25 = 251/4

= 52×14

= 312

= 25

= √5

So √5 is a surd of order 2 or a quadratic surd.














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.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Average | Word Problem on Average | Questions on Average

    May 19, 25 02:53 PM

    Worksheet on Average
    In worksheet on average we will solve different types of questions on the concept of average, calculating the average of the given quantities and application of average in different problems.

    Read More

  2. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More