document.write( "Question 334545: what is a radical
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Algebra.Com's Answer #239798 by jsmallt9(3758) $\"\"$ $\"About$

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Radicals are used to express roots in Math. For example, in $\"sqrt%285%29\"$ , everything but the 5 is a radical. The expression inside the radical is called the radicand. The number above and to the left of the radical is the index. There is no visible index in $\"sqrt%285%29\"$ . An \"invisible\" index like this is a \"2\".

\n" ); document.write( "In general a radical is used to express: the number which when raised to the index power results in the value of the radicand.

\n" ); document.write( "A radical with an index of 2 is called a square root. So $\"sqrt%285%29\"$ is read: \"square root of 5\". It represents the number which when raised to the power of 2 (squared) results in a 5. IOW, $\"sqrt%285%29%2Asqrt%285%29+=+5\"$ by definition.
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A radical with an index of 3 is called a cube root. So $\"root%283%2C+7%29\"$ is read: \"cube root of 7\". It represents the number which when raised to the power of 3 (cubed) results in a 7. IOW, $\"root%283%2C+7%29%2Aroot%283%2C+7%29%2Aroot%283%2C+7%29+=+7\"$ by definition.

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A radical with an index of 4 is called a fourth (4th) root. So $\"root%284%2C+20%29\"$ is read: \"fourth root of 20\". It represents the number which when raised to the 4th power results in a 20. IOW, $\"root%284%2C+20%29%2Aroot%284%2C+20%29%2Aroot%284%2C+20%29%2Aroot%284%2C+20%29+=+20\"$ be definition.

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A radical with an index of 5 is called a fifth (5th) root.

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A radical with an index of 6 is called a sixth (6th) root.

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etc.

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\n" ); document.write( "Many of these roots are irrational numbers. Irrational numbers are numbers which cannot be expressed as a fraction of integers. Nor can they be expressed as a decimal that terminates. They cannot even be expressed as a repeating decimal.

A \"famous\" irrational number is \"pi\": $\"pi\"$ . Just like we use the pi symbol, $\"pi\"$ , for that irrational number, we use the radical notation to indicate all the different kinds of roots. \n" ); document.write( "

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