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What are Surds and how to compare them?

Surds and their comparision

What are Surds and how to compare them?

Surds and their comparision

Here in this article detail is given that what are Surds and how to compare Surds. The surds are unresolved roots of a whole number,surds when simplified into a decimal number then the type of decimal we get is a non-recurrent decimal number, as an example √2= 1.4142135623730……, √3 =1.732050807568………, so in most of the real-time mathematical application to get a precise value we utilize surds and it is better to leave the result in the form of surds. Since Surds are non-recurrent decimal numbers so surds can not be written in the form of a fraction, it is that’s why surds are known as irrational numbers. The roots      etc are the examples of surds.

In straightway we can say Surds is an irrational number that cannot be represented in the form of fractions or recurring infinite decimals. So, in mathematical calculation, it can be left as a root. Surds are used in many real-time applications to make precise calculations. In this article, let us discuss different structures of surds and their simplification.

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Surds are the roots of numbers that cannot be simplified into a whole or rational number. It cannot be accurately represented in a fraction. In other words, a surd is a root of the whole number that has an irrational value.

The surds are written in the form of     where n is called the radical or order of the surds and x is a whole number whose nth roots can not be resolved.

Surds can be converted in the form of exponents as following

The rational numbers and the surds of the same degree can be compared easily by a straightforward way but for comparing surds of different degrees you needed a special technic.

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Surds of the same degree are known as equiradical surds and surds of unequal orders are known as non-equiradical surd

Comparison of equiradical or same order of surds:

If  x > y, then

Other examples: Write the following surds in ascending order

When the orders of surds (or radicand) are different but the whole numbers are the same

Since 8>4>3, therefore

ex: Which is greater between the following irrational number

7 is greater than 5 by 2 while 3 is greater than 2 by 1, so

or we can compare by a straight way because surds are of equal orders

7 +2 > 5 +3

Comparison of non-equiradical or different orders  of surds:

First of all converting them in to exponent form as following

Get the LCM of the all the radicants i.e 3,4,12 and converting them in to other surds of the same degree or radicals

  • The LCM of (3,4,12) is 12, converting the exponents in equivalent fractions of the lowest order

  • Placing these equivalent fractions in corresponding numbers.Now, the surds will become

  • Now comparing the numbers



NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number System Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial Chapter 10-Circles
Chapter 3- Coordinate Geometry Chapter 11-Construction
Chapter 4- Linear equations in two variables Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles Chapter 14-Statistics
Chapter 7-Triangles Chapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundings Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure? Chapter 10- Gravitation
Chapter3- Atoms and Molecules Chapter 11- Work and Energy
Chapter 4-Structure of the Atom Chapter 12- Sound
Chapter 5-Fundamental unit of life Chapter 13-Why do we fall ill ?
Chapter 6- Tissues Chapter 14- Natural Resources
Chapter 7- Diversity in living organism Chapter 15-Improvement in food resources
Chapter 8- Motion Last years question papers & sample papers

NCERT Solutions for class 10 maths

Chapter 1-Real number Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial Chapter 10-Circles
Chapter 3-Linear equations Chapter 11- Construction
Chapter 4- Quadratic equations Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression Chapter 13-Surface areas and Volume
Chapter 6-Triangle Chapter 14-Statistics
Chapter 7- Co-ordinate geometry Chapter 15-Probability
Chapter 8-Trigonometry

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Chapter 1- Chemical reactions and equations Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds Chapter 12- Electricity
Chapter 5-Periodic classification of elements Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process Chapter 14-Sources of Energy
Chapter 7-Control and Coordination Chapter 15-Environment
Chapter 8- How do organisms reproduce? Chapter 16-Management of Natural Resources

NCERT Solutions for class 11 maths

Chapter 1-Sets Chapter 9-Sequences and Series
Chapter 2- Relations and functions Chapter 10- Straight Lines
Chapter 3- Trigonometry Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations Chapter 15- Statistics
Chapter 8- Binomial Theorem  Chapter 16- Probability

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NCERT solutions for class 12 maths

Chapter 1-Relations and Functions Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions Chapter 10-Vector Algebra
Chapter 3-Matrices Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability Chapter 13-Probability
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Chapter 7- Integrals
Chapter 8-Application of Integrals

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