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Let's see some more problems and our step by step solver will simplify the radical expressions. THEOREM If a,b ∈ R, a>0, b>0, and n ∈ N then root(n,ab)=root(n,a)root(n,b). When nis an odd number and a0, a, k>0, we have root(n,m)=root(nk,a^mk), provided nk and mk∈ N. When nis an even number and a0, root(n,a)>0. When n is an even number and a>0, root(n,a)>0, called the principal root. It is a number whose nth power is a that is, (root(n,a))^n with the following conditions:ġ. For example,ĭEFINITION The nth root of a real number a is denoted by root(n,a). When n is an odd number, the nth power of a positive number is a positive number, and the nth power of a negative number is a negative number. When n is an even number, the nth power of a positive or a negative number is a positive number.
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