A. Radical Notation
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A. Radical Notation
Radical is from the Latin word radix meaning “root”.
In algebra, \(\sqrt[{n}]{x}\) indicates the \(n^{th}\) root of a quantity, the radicand (\(x\)).
Consider further that when the \(n^{th}\) root of \(x\) generates an answer, this same answer multiplied by itself \(n\) times yields \(x\).
For example, the \(n = {\color{red}2}\) root (also called the square root) of \(\color{red}16\) is the answer \(\color{red}4\). When \(\color{red}4\) is multiplied together \(\color{red}2\) times, the result is \(\color{red}16\). The index \(\color{red}2\) also represents the exponent when written in exponential form, \(\color{red}4^2 = 16\).
Recall that when the exponent in the radicand and the index are equal, the radical is equal to the base of the radicand. For example, \(\sqrt[{4}]{{3^4}} = 3\).
When Exponent and Index are Equal
In algebra, \(\sqrt[{n}]{x}\) indicates the \(n^{th}\) root of a quantity, the radicand (\(x\)).
Consider further that when the \(n^{th}\) root of \(x\) generates an answer, this same answer multiplied by itself \(n\) times yields \(x\).
For example, the \(n = {\color{red}2}\) root (also called the square root) of \(\color{red}16\) is the answer \(\color{red}4\). When \(\color{red}4\) is multiplied together \(\color{red}2\) times, the result is \(\color{red}16\). The index \(\color{red}2\) also represents the exponent when written in exponential form, \(\color{red}4^2 = 16\).
Recall that when the exponent in the radicand and the index are equal, the radical is equal to the base of the radicand. For example, \(\sqrt[{4}]{{3^4}} = 3\).
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When Exponent and Index are Equal
In general, for positive values of \(x\),
\(\sqrt[{n}]{x^n} = x\)
\(\sqrt[{n}]{x^n} = x\)