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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

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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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