Similar and Dissimilar Surds

We will discuss about similar and dissimilar surds and their definitions. 


Definition of Similar Surds:

Two or more surds are said to be similar or like surds if they have the same surd-factor.

                                                     or,

Two or more surds are said to be similar or like surds if they can be so reduced as to have the same surd-factor.

For example,

(i) √5, 7√5, 10√5, -3√5, 5\(^{1/2}\), 10 ∙ √5, 12 ∙ 5\(^{1/2}\) are similar surds;

(ii) 7√5, 2√125, 5\(^{2/5}\)are similar surds since 2√125 = 2 ∙ \(\sqrt{5 ∙ 5 ∙ 5}\) = 2√5 and 5\(^{5/2}\) =\(\sqrt{5^{5}}\) = \(\sqrt{5 ∙ 5 ∙ 5 ∙ 5 ∙ 5}\) = 25√5 i.e., each of the given surds can be expressed with the same surd-factor √5.

Definition of Dissimilar Surds:

Two or more surds are said to be dissimilar or unlike when they are not similar.

For example, √2, 9√3, 8√5, ∛6, 17, 7\(^{5/6}\) are unlike surds.


Note: A given rational number can be expressed in the form of a surd of any desired order.

For example, 4 = √16 = ∛64 = ∜256 = \(\sqrt[n]{4^{n}}\)

In general, if a he a rational number then,

x = √x\(^{2}\) = ∛x\(^{3}\) = ∜x\(^{4}\) = \(\sqrt[n]{x^{n}}\).









11 and 12 Grade Math

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