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Removing Radicals from the Denominator

by Jesi
(Toronto, Ontario, Canada)











































i am confused as to the steps of revomcing a radical from the denominator

Comments for Removing Radicals from the Denominator

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Sep 16, 2011
Rationalizing the Denominator
by: Staff

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Part II

The original problem used as the example is:

= 1/√(3)


“IF” the denominator could by multiplied by itself [the sqrt(3)], then the √ sign in the denominator would disappear, since:

√(3) * √(3) = √(3*3) = √(3²) = 3


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

To apply this concept, multiply the original fraction by √(3)/√(3). The fraction √(3)/√(3) is equal to 1, so the original fraction is merely being multiplied by 1. As you can see by the following illustration, its value has not been changed.


= [original fraction]

= [original fraction] * √(3)/√(3)

= [original fraction] * 1

= [original fraction]


Therefore,

= [original fraction] * √(3)/√(3)

= [(1)/√(3)] * [√(3)/√(3)]

When multiplying two fractions, multiply the both numerators and multiply the both denominators.

= [1 * √(3)] / [√(3) * √(3)]

= [1 * √(3)] / [√(3*3)]

= [1 * √(3)] / √(3²)

= [1 * √(3)] / 3


= √(3) / 3



The final answer is:

1 / √(3) = √(3) / 3




Thanks for writing.

Staff
www.solving-math-problems.com


Sep 16, 2011
Rationalizing the Denominator
by: S


Part I

The question:

by Jesi
(Toronto, Ontario, Canada)

i am confused as to the steps of revomcing a radical from the denominator


The answer:


Suppose you have a fraction which contains a radical in the denominator.

For example, the fraction 1 divided by the square root of 3 contains a radical in the denominator: 1/√(3).

You can rewrite this fraction so that the radical appears in the numerator, rather than in the denominator.

The fraction 1/√(3) can be rewritten as √(3)/3.

The decimal values of both fractions are exactly the same. 1/√(3) = 0.5773502691896. √(3)/3 = 0.5773502691896.

The process of rewriting the fraction 1/√(3) so the radical √(3) no longer appears in the denominator is called “Rationalizing the Denominator”.

“Rationalizing the Denominator” is the standard way of simplifying fractions which happen to contain radicals in the denominator.

I’m sure you are wondering what the point is.

Does it really matter if there is a radical in the denominator?

The answer is yes.

It does matter . . . rather, it did matter a great deal . . . before hand held calculators became widely available.

Before hand held calculators became widely available, arithmetic was usually completed by hand.

Try calculating the decimal value of 1/√(3) by hand.

First, look up the √(3) in a table of square roots. √(3) = 1.7320508075689.

Second, divide 1 by 1.7320508075689: 1 ÷ 1.7320508075689.

As you can see, without a calculator this arithmetic is very difficult. Not only is it difficult, it is easy for you to make a mistake.


Now consider the alternative.

When the fraction is rewritten as √(3)/3, the arithmetic is easy.

First, look up the √(3) in a table of square roots. √(3) = 1.7320508075689.

Second, divide 1.7320508075689 by 3: 1.7320508075689 ÷ 3. In this case the arithmetic is no problem at all.

Now that you know the reason for “Rationalizing the Denominator”, I’m going to show you how.

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