Question 334545
Radicals are used to express roots in Math. For example, in {{{sqrt(5)}}}, 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(5)}}}. An "invisible" index like this is a "2".<br>
In general a radical is used to express: the number which when raised to the index power results in the value of the radicand.<br>
<ul<li>A radical with an index of 2 is called a square root. So {{{sqrt(5)}}} 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(5)*sqrt(5) = 5}}} by definition.</li>
<li>A radical with an index of 3 is called a cube root. So {{{root(3, 7)}}} 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(3, 7)*root(3, 7)*root(3, 7) = 7}}} by definition.</li>
<li>A radical with an index of 4 is called a fourth (4th) root. So {{{root(4, 20)}}} is read: "fourth root of 20". It represents the number which when raised to the 4th power results in a 20. IOW, {{{root(4, 20)*root(4, 20)*root(4, 20)*root(4, 20) = 20}}} be definition.</li>
<li>A radical with an index of 5 is called a fifth (5th) root.</li>
<li>A radical with an index of 6 is called a sixth (6th) root.</li>
<li>etc.</li></ul>
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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.<br><br>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.