Bunuel wrote:
JackSparr0w wrote:
Bunuel wrote:
Official Solution:
The expression \(7 + \sqrt{48}\) can be rewritten as \(4 + 4\sqrt{3} + 3\) which is the same as \((2 + \sqrt{3})^2\). Therefore,\(\sqrt{7 + \sqrt{48}} - \sqrt{3} = 2 + \sqrt{3} - \sqrt{3} = 2\).
Answer: C
Is there anything specific here that we should pick up on, that would tell us that we should break up the problem this way?
the √48 can be broken down. I get that, and it seems intuitive enough. But is there a way to realize that we need to break the 7 into 4+3, and then use foil?
I guess Im just trying to figure out what the "real time" thought process should be when one sees this.
Thanks
I guess such kind of tricks should come with practice.
I came up with a generalized approach.
Visually superimpose the following form onto your expression (or sub-expression):
\(a±b\sqrt{c}\)
Then test to see if
\(\sqrt{a-c} = \frac{b}{2}\)
If so then you can rearrange your initial expression as
\((a-c) ± b\sqrt{c} + c\)
Try this with the problem example, where a = 7; b = 4; and c = 3
Also see with another example here:
\(14 + 6\sqrt{5}\)
a = 14
b = 6
c = 5
Test it:
\(\sqrt{14-5} = \frac{6}{2}\)
3 = 3
It passes the test, so we can rewrite the original expression as:
\(9 + 6\sqrt{5} + 5\)
Which can then be factored into
\((3+\sqrt{5})^2\)
I'm not sure if there are enough occurrences of this to justify memorizing this trick, but it's a tool you can use nonetheless.
I personally like Magsy's method.
close
55% (00:55) correct 
