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# What are Surds and how to compare them?

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

Therefore

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

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