SOLUTION: what is a radical

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Question 334545: what is a radical
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Radicals are used to express roots in Math. For example, in , 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 . An "invisible" index like this is a "2".

In general a radical is used to express: the number which when raised to the index power results in the value of the radicand.

A radical with an index of 2 is called a square root. So is read: "square root of 5". It represents the number which when raised to the power of 2 (squared) results in a 5. IOW, by definition.
  • A radical with an index of 3 is called a cube root. So is read: "cube root of 7". It represents the number which when raised to the power of 3 (cubed) results in a 7. IOW, by definition.

  • A radical with an index of 4 is called a fourth (4th) root. So is read: "fourth root of 20". It represents the number which when raised to the 4th power results in a 20. IOW, be definition.

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

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

  • etc.



    • 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": . Just like we use the pi symbol, , for that irrational number, we use the radical notation to indicate all the different kinds of roots.
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