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I got this question

Find the square root of $12+2\sqrt{6}$ expressing your answer in the form $\sqrt{m}+\sqrt{n}$.

I have no idea what this means and how to go about it.

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What is a surds? – Euler....IS_ALIVE Feb 3 '13 at 23:02
@Euler....IS_ALIVE Are you serious with that question? – Mob Feb 3 '13 at 23:04
Irrational root in American English. – Mob Feb 3 '13 at 23:05
It was a serious question. In 7 years of undergrad and graduate work, I've never seen that word. I googled it, but I am fairly confident that is an unusual word. Someone correct me if I'm wrong. – Euler....IS_ALIVE Feb 3 '13 at 23:06
@Euler....IS_ALIVE Quite usual, actually. – 1015 Feb 3 '13 at 23:07
up vote 6 down vote accepted

Let $x = \sqrt{12 + 2\sqrt{6}} = \sqrt{n} + \sqrt{m}$. Then $x^2 = 12 + 2\sqrt 6 = n + m + 2 \sqrt{nm}$.

Find $n$ and $m$ such that $n + m = 12$ and $nm = 6$.

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Can you expatiate on this? – Mob Feb 3 '13 at 23:13
Surdly you can solve the system of equations Damien has given. – Euler....IS_ALIVE Feb 3 '13 at 23:18

The answers for $n$ and $m$ are

$n = 6+\sqrt{30}$

$m = 6-\sqrt{30}$.

Notice that they are interchangable.

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