Simple and Compound Surds

We will discuss about the simple and compound surds.

Definition of Simple Surd:

A surd having a single term only is called a monomial or simple surd.

For example, each of the surds √2, ∛7, ∜6, 7√3, 2√a, 5∛3, m∛n, 5 ∙ 7^$$^{3/5}$$ etc. is a simple surd.

Definition of Compound Surd:

The algebraic sum of two or more simple surds or the algebraic sum of a rational number and simple surds is called a compound scud.

For example, each of the surds (√5 + √7), (√5 - √7), (5√8 - ∛7), (∜6 + 9), (∛7 + ∜6), (x∛y - b)  is a compound surd.

Note: The compound surd is also known as binomial surd. That is, the algebraic sum of two surds or a surd and a rational number is called a binomial surd.

For example, each of the surds (√5 + 2), (5 - ∜6), (√2 + ∛7) etc. is a binomial surd.

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