Question

How to justify the surds and how to find the surds are irratonal and rational numbers

Answer 1

Answer:

Rational number: A number of the form p/q, where p (may be a positive or negative integer or zero) and q (taken as a positive integer) are integers prime to each other and q not equal to zero is called a rational number or commensurable quantity.

Rational number: A number of the form p/q, where p (may be a positive or negative integer or zero) and q (taken as a positive integer) are integers prime to each other and q not equal to zero is called a rational number or commensurable quantity.Rational numbers are the numbers which can be expressed in the form of p/q where p is a positive or negative integer or zero and q is a positive or negative integer but not equal to zero.

Step-by-step explanation:

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Answer 2

Answer:

root of a positive real quantity is called a surd if its value cannot be exactly determined.

Surds are the irrational numbers which are roots of positive integers and the value of roots can’t be determined. Surds have infinite non-recurring decimals. Examples are √2, √5, ∛17 which are square roots or cube roots or nth root of any positive integer.

For example, each of the quantities √3, ∛7, ∜19, (16)^25 etc. is a surd.

note: All surds are irrationals but all irrational numbers are not surds. Irrational numbers like π and e, which are not the roots of algebraic expressions, are not surds.