An Algebra Puzzle

There are many ways one can solve this. It all boils down to what sort of techniques you are most comfortable with.

Now grab a pen and paper, and give this a go, When you are ready, keep reading for the solution.

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Solution

I am going to present this method of turning the insides of the square root into a perfect square.

The key is to decompose the 9 into 6 and 3.

Notice both of the insides are of the form a^2 -2ab + b^2 and a^2 + 2ab + b^2 respectively.

In our case, a is sqrt(6) and b is sqrt(3).

Then the squares and the roots cancel out.

So we get the following value.

How did you approach this problem. Let me and others know in the comments!

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