Rationalize the denominator, Mathematics

Rationalize the denominator for following.  Suppose that x is positive.

1311_Rationalize the denominator.png

Solution

We'll have to start this one off along with first using the third property of radicals to remove the fraction from underneath the radical as is needed for simplification.

1325_Rationalize the denominator1.png

Now, to get rid of the radical in the denominator we required the exponent on the x to be a 5.

It means that we have to multiply by417_Rationalize the denominator2.png thus let's do that.

1750_Rationalize the denominator3.png

Rationalizing the denominator may appear to have no real uses & to be honest we won't see many uses in an Algebra class.  However, if you are on a track which will take you into a Calculus class you will search that rationalizing is useful on occasion at that level.

Now at last we will discuss general version of the first property of radicals.  Recall that while first we wrote down the properties of radicals we needed that a positive number. It was done to make the work in this section a little simple. Though, with the first property that doesn't essentially have to be the case.

Here is the property for a general a (that means positive or negative)

1710_Rationalize the denominator4.png

 

where a  refer to the absolute value of a.  Absolute value always makes a positive number.

Thus, as a rapid example this means that,

287_Rationalize the denominator5.png

For square roots i.e

785_Rationalize the denominator6.png

Posted Date: 4/6/2013 2:18:20 AM | Location : United States







Related Discussions:- Rationalize the denominator, Assignment Help, Ask Question on Rationalize the denominator, Get Answer, Expert's Help, Rationalize the denominator Discussions

Write discussion on Rationalize the denominator
Your posts are moderated
Related Questions
Differentiate following functions.                       h (t ) = 2t 5 + t 2 - 5 / t 2 We can simplify this rational expression as follows.                       h (t )

The quotient of 3d 3 and 9d 5 is The key word quotient means division so the problem becomes 1d 3 -5/ 5. Divide the coef?cients:  1d 3 /3d-5 . While dividing like bases, subt


Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1) ?

Formulas for the volume of this solid V = ∫ b a A ( x) dx          V = ∫ d c A ( y ) dy where, A ( x ) & A ( y ) is the cross-sectional area of the solid. There are seve

how to add a fraction with an uncommon denomoninator

Find the are of the rectilinear.if it is the difference between to isosceles trapezoid whose corrsponding sides are parallel.

Properties of Vector Arithmetic If v, w and u are vectors (each with the same number of components) and a and b are two numbers then we have then following properties. v →


Extended product rule : As a last topic let's note that the product rule can be extended to more than two functions, for instance.  ( f g h )′ = f ′ gh + f g ′ h+ f g h′ ( f