convert √2 as sure of order 8
Answers
Step-by-step explanation:
The order of a surd indicates the index of root to be extracted.
In a−−√n, n is called the order of the surd and a is called the radicand.
For example: The order of the surd z√5 is 5.
(i) A surd with index of root 2 is called a second order surd or quadratic surd.
The surds which have the indices of root 2 are called as second order surds or quadratic surds. For example√2, √3, √5, √7, √x are the surds of order 2.
Example: √2, √5, √10, √a, √m, √x, √(x + 1) are second order surd or quadratic surd (since the indices of roots are 2).
(ii) A surd with index of root 3 is called a third order surd or cubic surd.
If x is a positive integer with nth root, then is a surd of nth order when the value of is irrational. In expression n is the order of surd and x is called as radicand. For example is surd of order 3.
The surds which have the indices of cube roots are called as third order surds or cubic surds. For example ∛2, ∛3, ∛10, ∛17, ∛x are the surds of order 3 or cubic surds.
Example: ∛2, ∛5, ∛7, ∛15, ∛100, ∛a, ∛m, ∛x, ∛(x - 1) are third order surd or cubic surd (since the indices of roots are 3).
(iii) A surd with index of root 4 is called a fourth order surd.
The surds which have the indices of four roots are called as forth order surds or bi-quadratic surds.
For example ∜2, ∜4, ∜9, ∜20, ∜x are the surds of order 4.
Example: 2–√4, 3–√4, 9–√4, 17−−√4, 70−−√4, a−−√4, m−−√4, x−−√4, x−1−−−−−√4 are third order surd or cubic surd (since the indices of roots are 4).
(iv) In general, a surd with index of root n is called a nth order surd.
Similarly the surds which have the indices of n roots are nth order surds. 2–√n, 17−−√n, 19−−√n, x−−√n are the surds of order n.
Example: 2–√n, 3–√n, 9–√n, 17−−√n, 70−−√n, a−−√n, m−−√n, x−−√n, x−1−−−−−√n are nth order surd (since the indices of roots are n).
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Step-by-step explanation:
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