Math Is Fun Forum

glenn101

Member

Registered: 2008-04-02

Posts: 108

Surds

ah, now ive just stumbled upon another surd question.

(√a+√b)²=a+b+2√ab

determine the square root of 17+6√8

can someone explain how to do this please?
I hope you can help,
thanks.

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Surds

(±(√a+√b))²=a+b+2√ab

the right side your squared term, the left side is your root squared.

so what you have to do is put 17+6√8 into the form a+b+2√ab

17+6√8 = 17+(2×3)√8 = 17+2√(8×9)

note now that, 17 = 8+9. and this is in the required form.

(√8+√9)²=8+9+2√(8×9)

which gives. √(17+6√8) = ±(√8 + √9)

Last edited by luca-deltodesco (2008-04-04 18:58:10)

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glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Surds

Thanks luca:D

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"If your going through hell, keep going."

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Surds

Here is a fun one.  What is:

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: Surds

yea that was neat

luca, the answer is NOT ±(√8 + 3), square roots are always positive

Last edited by Kurre (2008-04-06 04:23:22)

Roraborealis

Member

Registered: 2005-03-17

Posts: 1,594

Re: Surds

But what's all this thing about my Maths Teacher saying next year we'd be doing stuff on imaginary numbers? Like square roots of negative numbers?

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Surds

It's not too hard to understand imaginary numbers if you're good with surds.

Basically a new number "i" is introduced and defined to be √(-1), and all the same surd rules apply after that.
So for example, √(-9) =√9 x √(-1) = 3i.

Perhaps more importantly, i² = -1. That means imaginary things can sometimes combine and become real again.

For example, (4+i)(4-i). [Note - since those are real and imaginary numbers added together, I should technically be calling them 'complex']

Expand that like you would normally and you get 4² + 4i - 4i - i² = 4² - i² = 17.

Then later on you start representing imaginary numbers as a product of exponents and trig functions and other crazy things like that. It's great fun.

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Roraborealis

Member

Registered: 2005-03-17

Posts: 1,594

Re: Surds

Oooh! Sounds it.

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School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?