Hello everyone,

I'm learning math all over again and can't figure out how to solve this problem:

I know the answer to 9+2√18 = √6 + √3 from the back of the book but I don't know how to get there.

Any help is appreciated.

Regards,

Tymon

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- Feb 16th 2013, 05:28 AMTomstenFinding the square root of 9+2√18
Hello everyone,

I'm learning math all over again and can't figure out how to solve this problem:

I know the answer to 9+2√18 = √6 + √3 from the back of the book but I don't know how to get there.

Any help is appreciated.

Regards,

Tymon - Feb 16th 2013, 05:38 AMMINOANMANRe: Finding the square root of 9+2√18
this is a type of joke or what?

take (sqr6+sqr3)^2 and thats it...

MINOAS - Feb 16th 2013, 06:04 AMILikeSerenaRe: Finding the square root of 9+2√18
Hi Tymon! :)

Effectively you have the equation 9+2√18 = x^{2}and you want to know x.

There is no real straight forward way to do this, but you can use that (a+b)^{2}= (a^{2}+ b^{2}) + 2ab.

If a and/or b contains a square root, their squares won't, but 2ab will still contain a square root.

So we make the assumption that 2√18 matches 2ab and 9 matches (a^{2}+ b^{2}).

With a bit of trial and error we find that this works if we pick a=√6 and b=√3. - Feb 16th 2013, 07:21 AMSorobanRe: Finding the square root of 9+2√18
Hello, Tomsten!

Quote:

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- Feb 17th 2013, 02:53 AMibduttRe: Finding the square root of 9+2√18
- Feb 17th 2013, 09:01 AMpspssRe: Finding the square root of 9+2√18
√[9 + 2√18]

= √[9 + 2√6√3] ----------- it is first term and 2nd term of the form 2√a√b

= √[6 + 2√6√3 + 3] --------- write 9 as 6 + 3 to form middle term as 2√(6×3)

= √[√6 + √3]

= √6 + √3

---- - Feb 17th 2013, 11:58 AMTomstenRe: Finding the square root of 9+2√18
Thanks for all the quick and well worked out responses, everyone.

This has been hugely informative.