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# how to rationalise the denominator

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how to rationalise the denominator

Guest May 24, 2015

### Best Answer

#14
+90988
+8

Good question Zac,

If you look in the "Insert" drop down list, the second last one is "special characters"

The   √    is in t he 3rd row some of the indices are in there as well.

I was expecting to find pi in there but I cannot see it.

Now go to the fromat dropdown list.  There are all sorts of formating things in there including superscripts (powers) and subscripts.  If I was not using LaTex that is what I would use for powers.

If I wanted pi I would open up the [Math Formula] box and type in pi and hit Ok:)

Does that cover it ?

I see MG has given you LaTex solutions.  I have given you non-LaTex solutions   :)

oh, in latex pi is just \pi

Melody  May 24, 2015
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### 19+0 Answers

#1
+11752
+8

i think i know what you mean!

suppose youve got this " 1/√5 - √6" and have been told rationalise the denominator!

so we will do it like

1/(√5 -√6) x (√5 + √6)/(√5+√6)

this is how we rationalise!now according to the property (a+b)(a-b) = a^2 - b^2

so here also we will do it like this

= √5+√6/ (√5)^2 - (√6)^2

now becoz square can the root so we have

= √5 + √6/ 5 - 6

= √5 - √6/1

or

√5 - √6

that is how we rationalise the denominator!

rosala  May 24, 2015
#2
+90988
0

Thanks Rosala but $$\sqrt5-\sqrt6$$   already has a rational denominator.  It is one!

$$\sqrt5-\sqrt6=\frac{\sqrt5-\sqrt6}{1}$$

Melody  May 24, 2015
#3
+981
+5

Nice :)

Here are a couple of examples (a denominator with a surd in it is irrational)

$$\frac{1}{\sqrt{5}} = \frac{1}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{5}}{5} = 5$$   (we can do this because sqrt5/sqrt5 = 1)

Using Rosla's example:

1/(√5 -√6) x (√5 + √6)/(√5+√6)   ([√5+√6] is the conjugate of [√5 -√6])

(√5 + √6)/(√5 -√6)(√5+√6)

(√5 + √6)/(√5^2 - √6^2)  (as Rosala said we can do this beacuse (a-b)(a+b) = a^2 - b^2, meaning all the                                           surds in the denominator are cancelled out)

(√5 + √6)/(5 - 6)

(√5 + √6)/-1   or

-(√5 + √6)/1  or

-√5  -√6

zacismyname  May 24, 2015
#4
+11752
0

but melody ive learnt this way only!!!;//

anyways ive edited it

rosala  May 24, 2015
#5
+11752
0

melody you gave me three points....how did it become 1

rosala  May 24, 2015
#6
+90988
+5

That is better Rosala but both you and Zac need more brackets on the denominator :/

And

you need more on the numerator as well Rosala.

e.g.

= √5+√6/ (√5)^2 - (√6)^2

should be      = (√5+√6)/ ((√5)^2 - (√6)^2)

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

I think that you can lay this out much more nicely using the Maths formula button.

(I would use LaTex but it is slightly more difficult to learn)

lets see.

Here is a line that I copied off Rosala

1/(√5 -√6) x (√5 + √6)/(√5+√6)

I will try entering it like this

1/(sqrt(5)-sqrt(6))*((sqrt(5)+sqrt(6)/(sqrt(5)-sqrt(6)))

Mathematically speaking the blue brackets are not needed.

They just make it present better using the [Maths Formula] input button

$${\frac{{\mathtt{1}}}{\left({\sqrt{{\mathtt{5}}}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{6}}}}\right)}}{\mathtt{\,\times\,}}\left({\frac{\left({\sqrt{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{6}}}}\right)}{\left({\sqrt{{\mathtt{5}}}}{\mathtt{\,-\,}}{\sqrt{{\mathtt{6}}}}\right)}}\right)$$

you both gave it a good shot though.  3 points each       (I hope that you get to keep them )

Melody  May 24, 2015
#7
+11752
0

Thank you Melody....the truth is most of latex goes above my head so i mostly avoid it...beco of mathsgod ive learnt a bit....but i forget it.....anyways thanks...the way i solved the problem was the one i learnt......thats what we are taught!

rosala  May 24, 2015
#8
+90988
+5

I DID NOT USE ANY LATEX THERE ROSALA!

I DID IT WITH THE MATHS FORMULA INPUT BUTTON WHICH IS MUCH EASIER TO LEARN!

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

You solved the problem correctly but you needeD more brackets.

You wrote.

= √5+√6/ (√5)^2 - (√6)^2

this means

= √5+√6/ (√5)^2 - (√6)^2  =     $${\sqrt{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\sqrt{{\mathtt{6}}}}}{{{\sqrt{{\mathtt{5}}}}}^{\,{\mathtt{2}}}}}{\mathtt{\,-\,}}{{\sqrt{{\mathtt{6}}}}}^{\,{\mathtt{2}}}$$

Whereas what you meant was

= (√5+√6)/( (√5)^2 - (√6)^2)      =    $${\frac{\left({\sqrt{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{6}}}}\right)}{\left({{\sqrt{{\mathtt{5}}}}}^{\,{\mathtt{2}}}{\mathtt{\,-\,}}{{\sqrt{{\mathtt{6}}}}}^{\,{\mathtt{2}}}\right)}}$$

SEE - YOU NEEDED MORE BRACKETS!

Melody  May 24, 2015
#9
+11752
0

but melody.....when i write it in my copy...its correct...my every teacher says it we do it like this only...we write the root nin bracket and square outside and cut them!idk whats the problem!

rosala  May 24, 2015
#10
+90988
0

I would think that when you write it by hand it is automatically written as a fraction.

So it is clear what is on the bottom and what is on the top.

When you do a keyboard entry like you did that visual clarity has gone and you have to spell out exactly what you mean with brackets.

This is your one

= √5+√6/ (√5)^2 - (√6)^2  =  $${\sqrt{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\sqrt{{\mathtt{6}}}}}{{{\sqrt{{\mathtt{5}}}}}^{\,{\mathtt{2}}}}}{\mathtt{\,-\,}}{{\sqrt{{\mathtt{6}}}}}^{\,{\mathtt{2}}}$$

Now I am going to do the other one with latex because I can make it look EXACTLY like it should look when  you write it by hand.  (I am not expecting you to care about the LaTex)

This is what it should be

= (√5+√6)/( (√5)^2 - (√6)^2)      =       $$\frac{\sqrt5+\sqrt6}{\sqrt5^2-\sqrt6^2}$$

See, if you want all that first stuff on the top AND all that second lot of stuff on the bottom

THEN you need to show this with the brackets!

REMEMBER:     PEDMAS

If there are no brackets then you MUST do the division BEFORE you do the addition or the subtraction.

That is why you need the brackets.

Melody  May 24, 2015
#11
+4663
0

This looks intresting.

MathsGod1  May 24, 2015
#12
+981
0

Thanks you are right about the brackets. I would have used latex (I did for my first example) but it would have been around 10 lines long and I was feeling lazy.

I have a question though . . .

How do people type √ (I copied that)? Also I see pi and powers used regularly but I don't understand how they do it . . . is it a keyboard thing?

zacismyname  May 24, 2015
#13
+4663
+8

Using Maths Formula and Calculations it is seen as sqrt(number)

E.g.

$${\sqrt{{\mathtt{10}}}}$$        sqrt(10)

In Latex it is shown as this: \sqrt{number} (The { } are really important as it lengthens the lines for longer numbers)

This is when using ( ) instead of { }

$$\sqrt(1000000000)$$                     \sqrt(1000000000)

This is the right way.

$$\sqrt{1000000000}$$                              \sqrt{1000000000}

Powers on Formulas and Calculations are showed as (Number)^(to the power of)

$${{\mathtt{10}}}^{{\mathtt{10}}}$$                   10^10

Latex is slightly different, it uses { } on the power of so number

Using { }

$$10^{10}$$            10^{10}

As for Pi I'm not sure for the exact digits as i don't use it but you can just type 3.14 (i think)

MathsGod1  May 24, 2015
#14
+90988
+8
Best Answer

Good question Zac,

If you look in the "Insert" drop down list, the second last one is "special characters"

The   √    is in t he 3rd row some of the indices are in there as well.

I was expecting to find pi in there but I cannot see it.

Now go to the fromat dropdown list.  There are all sorts of formating things in there including superscripts (powers) and subscripts.  If I was not using LaTex that is what I would use for powers.

If I wanted pi I would open up the [Math Formula] box and type in pi and hit Ok:)

Does that cover it ?

I see MG has given you LaTex solutions.  I have given you non-LaTex solutions   :)

oh, in latex pi is just \pi

Melody  May 24, 2015
#15
+981
+5

yes thank you :) Now I really feel like part of the forum :)

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zacismyname  May 24, 2015
#16
+90988
0

Oh, you are very much a part of this forum Zac    LOL

But now I guess you can 'swear' at people with more 'colourful' symbols

MathsGod1,

You cannot write an irrational number such as   $${\sqrt{{\mathtt{3}}}}$$    in digits.  NO irrational number can be expressed in digits.  You can get an estimate from the calculator but it is an estimate.  It will never be an exact value!

Melody  May 24, 2015
#17
+11752
0

#

'swear' at people with more 'colourful' symbols

#

now that is what i call a grown-up brain !ROFLOL!

rosala  May 24, 2015
#18
+90988
0

Oh yes Rosala, you said I am only good at 'grown up' humour.   That is really funny you know.    LOL

Melody  May 24, 2015
#19
+11752
0

ofcourse you are...the queen of witty thoughts!haha

rosala  May 24, 2015

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