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 surdfactor.
or,
Two or more surds are said to be similar or like surds if they can be so reduced as to have the same surdfactor.
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 surdfactor √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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