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Rationalize the Denominator of sqrt{(2x)/(3c⁴)}










































Rationalize the Denominator of the square root of a fraction

Rationalizing the denominator is equivalent to saying: change the number in the denominator from an irrational number (in this case a square root) to a rational number (a number without a fractional exponent).

Rationalize the denominator of √{(2x)/(3c⁴)}

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Sep 24, 2012
Rationalize the Denominator
by: Staff

Answer:

Part I


√{(2x) / (3c⁴)}

= {√(2x) / √(3c⁴)}

Rationalizing the denominator means removing the square root sign √ from the denominator (so that the denominator becomes a rational number).

To accomplish this, multiply the denominator √(3c⁴)by itself √(3c⁴).

√(3c⁴)*√(3c⁴)

= √(3*3*c⁴*c⁴)

= 3*c⁴

= 3c⁴

However, in order to preserve the value of the original fraction, both the numerator and denominator must each be multiplied by the same amount: √(3c⁴).

To apply this concept, multiply the original fraction by {√(3c⁴)/√(3c⁴)}.

The fraction {√(3c⁴)/√(3c⁴)} is equal to 1, so the original fraction is merely being multiplied by 1.

As you can see by the following illustration, the value of the original fraction has not been changed.


= [original fraction]

= [original fraction] * {√(3c⁴)/√(3c⁴)}

= [original fraction] * 1

= [original fraction]


Therefore,

= [original fraction] * 1

           √(2x)
= --------------------------- * 1
           √(3c⁴)


           √(2x)                          √(3c⁴)
= --------------------------- * ------------------
           √(3c⁴)                         √(3c⁴)



---------------------------------------------------

Sep 24, 2012
Rationalize the Denominator
by: Staff


---------------------------------------------------

Part II


Multiply both numerators and multiply both denominators, just as you would when multiplying any two fractions:


       √(2x) * √(3c⁴)
= ---------------------------
      √(3c⁴) * √(3c⁴)



       √(2x) * √(3c⁴)
= ---------------------------
             (3c⁴)



       √(2x) * c²√(3)
= ---------------------------
             (3c⁴)


Cancel the exponents for the variable “c” to the extent that you can


       √(2x) * c²⁻²√(3)
= ---------------------------
             (3c⁴⁻²)



       √(2x) * c⁰√(3)
= ---------------------------
             (3c²)



       √(2x) * 1√(3)
= ---------------------------
             (3c²)



       √(2x) * √(3)
= ---------------------------
             (3c²)



            √(6x)
= ---------------------------
             (3c²)




Final Answer:


                 = {√(6x) / (3c²)}



Thanks for writing.

Staff
www.solving-math-problems.com


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