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glenn101

Member

Registered: 2008-04-02

Posts: 108

Surds - Rationalising The Denominator

Hi, this is my first post.
I am having trouble with rationalising the denominator, it is really frustrating, here are some example questions of which I am finding hard to complete.

2√3-1/
√2

√5+2/
√5-2

√3+√2/
√3-√2

could you please show me the steps in answering these questions.

Thanks in advance,
Glenn

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Surds - Rationalising The Denominator

im guessing you mean:

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Surds - Rationalising The Denominator

For the first one, multiply top and bottom by √2

For question 2 and 3 you can use the general technique of multiplying by the denomitor, but with the sign reversed. i.e for example.

Last edited by luca-deltodesco (2008-04-02 19:41:31)

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glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Surds - Rationalising The Denominator

yes, that is what I mean.
This is what I got so far however it is still not the right answer:(

according to the book the answer is 4root5+9
what am I doing wrong? please help.

Last edited by glenn101 (2008-04-02 22:14:00)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Surds - Rationalising The Denominator

You're right up to where you are, you just needed to carry on a bit longer.

Expanding the brackets in the numerator gives (√5)² + 2√5 + 2√5 + 2²
= 5 + 4√5 + 4 = 9 + 4√5.

Obviously, the denominator becomes 1, and so 4√5 + 9 is your answer.

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glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Surds - Rationalising The Denominator

Thank you mathsyperson and Luca:) it makes much more sense now.
I have worked out correctly questions 1&2 but question 3 I still am not getting correct.

√3+√2/      √3+√2/   √3+√2/      (√3)²+(√2)²/     ?/
√3-√2   =   √3-√2 x √3+√2  =       3   +  2       =  5

thats as far as I got, the answer is 2√6+5

I got the 5 but the numerator confuses me.

Last edited by glenn101 (2008-04-03 13:43:04)

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Surds - Rationalising The Denominator

The denominator is actually 1 again. It works out as 3-2 instead of 3+2.

For the numerator, you just do the same thing as I showed above. There are two surds there this time, but it doesn't change the method.

(√3 + √2)² = (√3)² + 2√3√2 + (√2)²
= 5 + 2√6.

As before, since the denominator works out to be 1, the final answer is equal to the numerator.

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It wanted to be normal.

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Surds - Rationalising The Denominator

ok I see what I've done wrong again thanks very much:)

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mujeeb khader

Guest

Re: Surds - Rationalising The Denominator

simplify again u will get the answer in the book like
   9 + 4√5