Radicals ExpressionsRadicals Expressions

By Khalil DeloatchBy Khalil Deloatch

Radicals ExpressionsRadicals Expressions

• A radical expression is an expression A radical expression is an expression containing a square root. containing a square root.

• The symbol that is used to denote The symbol that is used to denote square root or nth roots. square root or nth roots. Radicand: Radicand is a number or Radicand: Radicand is a number or expression inside the radical symbol. expression inside the radical symbol.

Radicals ExpressionsRadicals Expressions

• Radical equation: An equation Radical equation: An equation containing radical expressions with containing radical expressions with variables in the radicands. variables in the radicands. Radical inequality: An inequality Radical inequality: An inequality containing a radical expression with containing a radical expression with the variable in the radicand. the variable in the radicand.

ExamplesExamples

• Example 1: Use the Example 1: Use the product rule to product rule to multiply. Note that both multiply. Note that both radicals have an index radicals have an index number of 3, so we number of 3, so we were able to put their were able to put their product together under product together under one radical keeping the one radical keeping the 3 as its index number.  3 as its index number.  Since we cannot take Since we cannot take the cube root of 6 and the cube root of 6 and 6 does not have any 6 does not have any factors we can take the factors we can take the cube root of, this is as cube root of, this is as simplified as it gets.simplified as it gets.

• MultiplyMultiply

ExamplesExamples

• Example 2: Use the : Use the product rule to multiply. product rule to multiply. Note that both radicals Note that both radicals have an index number of have an index number of 4, so we were able to put 4, so we were able to put their product together their product together under one radical keeping under one radical keeping the 4 as its index number.  the 4 as its index number. 

• Since we cannot take the Since we cannot take the fourth root of what's fourth root of what's inside the radical sign and inside the radical sign and 10 does not have any 10 does not have any factors we can take the factors we can take the fourth root of, this is as fourth root of, this is as simplified as it gets.simplified as it gets.

• MultiplyMultiply

Question?Question?

• Solve the problem: Solve the problem:

ResourcesResources

• http://www.wtamu.edu/academic/annhttp://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_s/mps/math/mathlab/int_algebra/int_alg_tut39_simrad.htmalg_tut39_simrad.htm

• http://www.icoachmath.com/math_dihttp://www.icoachmath.com/math_dictionary/Radical_Expression.htmlctionary/Radical_Expression.html

• http://teachers.henrico.k12.va.us/mahttp://teachers.henrico.k12.va.us/math/hcpsalgebra2/5-6.htmth/hcpsalgebra2/5-6.htm

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