  # multiply, add, subtract, and divide radicals

by Bethany
(Colorado Springs, Co)

Can i get an example on how to multiply, add, subtract, and divide radicals

### Comments for multiply, add, subtract, and divide radicals

 Aug 25, 2011 Radicals: Adding, Multiplying, Dividing by: Staff The question: by Bethany (Colorado Springs, Co) Can i get an example on how to multiply, add, subtract, and divide radicals The answer: The first thing to remember is that radicals and exponents are related. For example: √(x) = x^(1/2) = x^(.5) ∛(x) = x^(1/3) = x^(.33333333333…) ∜(x) = x^(1/4) = x^(.25) Because of this correspondence, the rules you learned about adding, dividing, and multiplying exponents apply to radicals as well. Addition (examples): Terms containing exponents can only be added if the base AND the exponents are the same. In the following two examples, the base is x, and the exponents are the same. x³ + 2x³ = 3x³ x^(.5) + 2x^(.5) = 3x^(.5) In this example, the base is the same, but the exponents are not the same. The terms cannot be added. x³ + 2x² = x³ + 2x² In this example, the base is not same, but the exponents are the same. The terms cannot be added. x³ + 2y³ = x³ + 2y³ Terms containing radicals can only be added if the radicand and the index are the same. In the following two examples, the radicand is x, and the index is the same. √(x)+ 2√(x)= 3√(x) ∛(x) + 5∛(x) = 5∛(x) In this example, the radicand is the same, but the index is not the same. The terms cannot be added. ∛(x) + 5∜(x) = ∛(x) + 5∜(x) In this example, the radicand is not same, but the index is the same. The terms cannot be added. ∛(x) + 5∛(y) = ∛(x) + 5∛(y) Multiplying terms containing Exponents or Radicals is much easier. Multiplying exponents when the base is the same: just add the exponents x³ * 2x³ = 2x³⁺³ = 2x⁶ x^(.5) * 2x(.5) = 2x^(.5+.5) = 2x¹= 2x Multiplying exponents when the base of each factor is not the same: x³ * 2y³ = 2x³y³ x^(.5) * 2y(.5) = 2x^(.5)2y^(.5) Multiplying radicals when the radicand and the index are the same: ∛(x) * 5∛(x) = 5∛(x*x) = 5∛(x²) = 5x^(2/3) = 5x^(.66666666…) √x * 2√x = 2√(x*x) = 2√(x²) = 2x Multiplying radicals when the radicand of each factor is not the same: ∛(x) * 5∛(y) = 5∛(x*y) = 5∛(xy) Dividing terms containing Exponents or Radicals is similar to multiplication. Dividing exponents when the base is the same: just subtract the exponents 2x³ ÷ x² = 2x³⁻² = 2x¹ = 2x 2x^(.5) ÷ 2x^(.1) = 2x^(.5-.1) = 2x^(.4) Dividing radicals when the variable and the index are the same: 5∛(3x) ÷ ∛(x) = 5∛(3x÷x) = 5∛(3) 2√x ÷ √x = 2√(x÷x) = 2√(1) = 2 Thanks for writing. Staff www.solving-math-problems.com

 Nov 08, 2013 Radicals. by: Anonymous You people are great, thank you for your help.

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