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help with simplifying and rationalising

Hi all,

I am trying this as a last ditch attempt to understand what is in likely hood really simple! I am undertaking a course to allow me to develop maths further within the course I teach which is construction. This week we have been looking at simplifying and rationalizing surds the first question I did was easy :

6 root 5 6 root 5
-- x ------ = -------
root 5 root 5 5

but the next question is

2 root 3
_______
root 7

As there two roots presume still multiply by the denominator but what do I do with the surd at the top?

Any help will be most gratefully received as have tried you tube videos but none show this variant either as first example or with addition multiplication involved in the denominator.
Thanks Craig
I'm not sure I quite understand your question, could you elaborate further? In terms of rationalising the denominator, whatever you do to the bottom, you must do to the top also. So if you're multiplying the bottom by something, you need to multiply the top by it too.

After simplifying, if you still have a surd at the top, that's absolutely fine. The whole point of rationalising the denominator is to remove the surd from the bottom. It isn't to remove the surd on top of the fraction because that's not a problem in terms of working with the fraction. :h:
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Avatar for Alex621
Alex621
17
Original post by craigleach
Hi all,

I am trying this as a last ditch attempt to understand what is in likely hood really simple! I am undertaking a course to allow me to develop maths further within the course I teach which is construction. This week we have been looking at simplifying and rationalizing surds the first question I did was easy :

6 root 5 6 root 5
-- x ------ = -------
root 5 root 5 5

but the next question is

2 root 3
_______
root 7

As there two roots presume still multiply by the denominator but what do I do with the surd at the top?

Any help will be most gratefully received as have tried you tube videos but none show this variant either as first example or with addition multiplication involved in the denominator.
Thanks Craig


Yes, still multiply the denomiator and numerator by root 7, so on the top you will have (2root3) x (root7). Do you know how to simplify this?
Original post by craigleach
Hi all,

I am trying this as a last ditch attempt to understand what is in likely hood really simple! I am undertaking a course to allow me to develop maths further within the course I teach which is construction. This week we have been looking at simplifying and rationalizing surds the first question I did was easy :

6 root 5 6 root 5
-- x ------ = -------
root 5 root 5 5

but the next question is

2 root 3
_______
root 7

As there two roots presume still multiply by the denominator but what do I do with the surd at the top?

Any help will be most gratefully received as have tried you tube videos but none show this variant either as first example or with addition multiplication involved in the denominator.
Thanks Craig


2 √ 3
---------
√7. So firstly multiply both the numerator and denominator by √7.

This will give: (2√3)(√7) divided by 7. (2√3)(√7)=(2√21) numerator, with 7 remaining as the denominator. This means our answer is 2√(3/7).

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