what was a surd give an example
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In mathematics, an nth root of a number x, where n is usually assumed to be a positive integer, is a number r which, when raised to the power n yields x:
{\displaystyle r^{n}=x,} {\displaystyle r^{n}=x,}
where n is the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc.
For example:
3 is a square root of 9, since 32 = 9.
−3 is also a square root of 9, since (−3)2 = 9.
Any non-zero number, considered as complex number, has n different "complex roots of degree n" (nth roots), including those with zero imaginary part, i.e. any real roots. The root of 0 is zero for all degrees n, since 0n = 0. In particular, if n is even and x is a positive real number, one of its nth roots is positive, one is negative, and the rest (when n > 2) are complex but not real; if n is even and x is a negative real, none of the nth roots is real. If n is odd and x is real, one nth root is real and has the same sign as x, while the other (n − 1) roots are not real. Finally, if x is not real, then none of its nth roots is real
{\displaystyle r^{n}=x,} {\displaystyle r^{n}=x,}
where n is the degree of the root. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc.
For example:
3 is a square root of 9, since 32 = 9.
−3 is also a square root of 9, since (−3)2 = 9.
Any non-zero number, considered as complex number, has n different "complex roots of degree n" (nth roots), including those with zero imaginary part, i.e. any real roots. The root of 0 is zero for all degrees n, since 0n = 0. In particular, if n is even and x is a positive real number, one of its nth roots is positive, one is negative, and the rest (when n > 2) are complex but not real; if n is even and x is a negative real, none of the nth roots is real. If n is odd and x is real, one nth root is real and has the same sign as x, while the other (n − 1) roots are not real. Finally, if x is not real, then none of its nth roots is real
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