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
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
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.