Positive \({n^{\text{th}}}\) Root
Positive \({n^{\text{th}}}\) Root
\(3\times 3={{3}^{2}}\) | \(=9\) | \({{3}^{2}}=9\) \(\therefore \sqrt{9}=3\) (Square Root)
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|---|---|---|
\(3\times 3\times 3={{3}^{3}}\)
| \(=27\) | \({{3}^{3}}=27\) \(\therefore \sqrt[3]{27}=3\) (Cube Root) |
\(3\times 3\times 3\times 3={{3}^{4}}\) | \(=81\) | \({{3}^{4}}=81\) \(\therefore \sqrt[{}]{81}=3\) (_________ Root) |
\(3\times 3\times 3\times 3\times 3={{3}^{5}}\) | \(=243\) | \({{3}^{5}}=243\) \(\therefore \sqrt[{}]{243}=3\) (_________ Root)
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\({a = b^n}\) | ||
In general, if \(a\) is a positive number such that \(a={{b}^{n}}\) for some positive real number \(b\) and positive integer \(n\), then \(b\) is the positive n\(^{th}\) root of \(a\) and we write
\(b=\sqrt[n]{a}\)
An expression that involves the radical sign \(\sqrt[n]{\,\,\,\,\,}\) is called the radical expression.
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