Bunuel wrote:

teal wrote:

How can I use estimation to solve this? I tried using estimation ...but always get trapped in some wrong choice....what to do avoid getting a wrong answer when using estimation in a question that has answer choices that are too close?

The question should read.

\(\sqrt{7+\sqrt{48}}-\sqrt{3}=?\)

A. 1

B. 1.7

C. 2

D. 2.4

E. 3

\(\sqrt{7+\sqrt{48}}=\sqrt{7+4\sqrt{3}}=\sqrt{4+4\sqrt{3}+3}=\sqrt{(2+\sqrt{3})^2}=2+\sqrt{3}\).

So, \(\sqrt{7+\sqrt{48}}-\sqrt{3}=2+\sqrt{3}-\sqrt{3}=2\).

Answer: C.

P.S. It's not a good idea to use approximation for this question.

Bunuel, what is wrong with using approximation for this question, because aside from using the technique that you just used, it is the only method left?

I did the following and answered the question correctly.

sqrt(48) ~ sqrt(49) = 7

sqrt(7+sqrt(48)) - sqrt(3)=

sqrt(14) - sqrt(3)

sqrt(9) < sqrt(14) < sqrt(16)

3 < sqrt(14) < 4

We know that sqrt(14) is closer to 4 than it is to 3, so let's try some numbers.

Given that the answer choices are numbers with only a tenths place, we can estimate sqrt(14) to a number to just the tenths place.

sqrt(14) ~ 3.8

3.8^2 = 14.44 | Close enough

3.8-sqrt(3) = 3.8 - 1.7 = 2.1

The closest answer to this is 2.

C