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<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>
<a https://www.thestudentroom.co.uk/showthread.php?t=7467335'> Year 12s: what will be the first way you research your future options? >>

"Simplify 5āˆš2 / 3-āˆš2. Give your answer in the form b+cāˆš2 / d"

Please help me learn how to answer this! :smile:

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you multiply top and bottom by 3 + āˆš2
Original post by elliepollylu
Please help me learn how to answer this! :smile:


Are you looking for other people to do all of your homework? :/

As the bear said, multiply top and bottom by 3 + āˆš2 and then simplify.
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S27
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Can you use brackets just so i know exactly what you mean.
The reason you multiply by 3 + āˆš2 is so that the denominator becomes the difference of two squares and so the roots disappear. The process is called rationalising the denominator ... ie remove the irrational surds.
(edited 8 years ago)
Original post by the bear
you multiply top and bottom by 3 + āˆš2


Can I ask where you got 3+āˆš2 from? :smile:
Original post by Hydeman
Are you looking for other people to do all of your homework? :/

As the bear said, multiply top and bottom by 3 + āˆš2 and then simplify.


I'm really not trying to get other people to do my homework for me, I'm just trying to understand how to answer the questions :/
Original post by elliepollylu
Can I ask where you got 3+āˆš2 from? :smile:


See Muttley79's answer. :wink:

Original post by Muttley79
The reason you multipy by the complex conjugate is so that the denominator becomes the difference of two squares and so the roots disappear. The process is called rationalising the denominator ... ie remove the irrational surds.


It's basically multiplying both by the denominator but with the signs reversed.
Original post by elliepollylu
Can I ask where you got 3+āˆš2 from? :smile:


Did you read my post?

You multiply the numerator and denominator by the complex conjugate.
Original post by Muttley79
Did you read my post?

You multiply the numerator and denominator by the complex conjugate.


Thank you very much :smile:
Original post by Hydeman
See Muttley79's answer. :wink:



It's basically multiplying both by the denominator but with the signs reversed.


Thank you :smile:
Original post by elliepollylu
Thank you very much :smile:


Post your working if you don't get the answer in the book.

It's a really neat technique much loved by the examiners :smile:
I've done it and showed my working out in two steps in the attached file. sorry I've done step 2 wrong let me do it again i've probably confused you more
(edited 8 years ago)
Untitled.png18.0KB
You also need to know your surd rules thoroughly to do this question
It's called rationalizing the denominator if you wanted to read up about it
Original post by Muttley79
The reason you multipy by the complex conjugate is so that the denominator becomes the difference of two squares and so the roots disappear. The process is called rationalising the denominator ... ie remove the irrational surds.

Original post by elliepollylu
Thank you :smile:

You're not multiplying by the complex conjugate; there is no 'i' involved here. You're simply rationalising the denominator. The complex conjugation of a number, say, a+bi, is a-bi, so if we had a fraction like (3+5i)/(2+i), then yes, we would multiply top and bottom by 2-i, the complex conjugate of 2+i.
Original post by yl95
You're not multiplying by the complex conjugate; there is no 'i' involved here. You're simply rationalising the denominator. The complex conjugation of a number, say, a+bi, is a-bi, so if we had a fraction like (3+5i)/(2+i), then yes, we would multiply top and bottom by 2-i, the complex conjugate of 2+i.


Well it is effectively the same idea - just no i component :smile:
Original post by Muttley79
Well it is effectively the same idea - just no i component :smile:


Yes, but the wrong terminology, just in case the student decided to use 'complex conjugate' to describe this.
Here's the corrected step 2
Untitled.png19.3KB
Original post by yl95
Yes, but the wrong terminology, just in case the student decided to use 'complex conjugate' to describe this.


You're right. The correct term in this case is conjugate, not complex conjugate.

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