What is the value of (\sqrt{7+\sqrt29}-\sqrt{7-[

is there a quick way to solving these kind of questions? Even though I use the (x-y)^2 formula, it takes me a good 5 minutes..

The above method is the fastest. Should take no more than 1-1.5 minutes.

Why are we using a^2 as square root of 49 and not as 7. How can I know that I need to keep one root as in 2[square_root]49-29

Instead of 2 (7 - [square_root]29) ???

I've been going over this and can't seem to wrap my head around this part:

(\sqrt{7+[square_root]29}[/square_root])^2 <---- isn't this another a^2 + b^2 + 2ab? why did this reduce to just 7+\sqrt{29}?

\((\sqrt{x})^2=\sqrt{x}*\sqrt{x}=x\).

Similarly: \((\sqrt{7+\sqrt{29}})^2=\sqrt{7+\sqrt{29}}*\sqrt{7+\sqrt{29}}=7+\sqrt{29}\)

Thanks! I see my error. Since the sq rt covers the whole (7+29), that is to be treated as one term, NOT two, so it is not A^2 + 2ab + b^2, it is just that term multiplied by itself.

Bunuel way is the best approach but you can also use estimation if you are short on time. Looking at the answer choices, they are spread out far enough to estimate.

5^2 = 25 and 6^2 = 36. So estimate the sqrt29 to be 5.5.

Now 7 + 5.5 = 12.5 and 7 -5.5 = 1.5.
3^2 = 9 and 4^2 = 16. So estimate the sqrt12.5 to be 3.5 and Sqrt1.5 to be a little more than 1, or just assume 1.

Not you have (3.5 -1)^2 = 6.something

Looking at the answer choices, you can immediately cross of A (too small), D and E (too big).
Now you are left between b and C. If you notice b has sqrt 29, which you already assumed to be 5.5. Multiplying it by 2 will give you a number greater than 10. Answer C looks good because you have 14 - 4*2.something. This value will be closer to 6

Answer C

I am generally quite good at quant (48<), but I am terrible at simplifying. I always get stuck. Spent an inordinate amount of time on this question, and I still was way of target. Any tips for how to improve?

Thank you!!

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