Bunuel wrote:

If \(\sqrt{17+\sqrt{264}}\) can be written in the form \(\sqrt{a}+\sqrt{b}\) , where a and b are integers and b < a, then a - b =

A. 1

B. 2

C. 3

D. 4

E. 5

Kudos for a correct solution.

At first we see that we can't calculate result of this expression \(\sqrt{17+\sqrt{264}}\)

So we should eliminate the root by powering equation

\((\sqrt{17+\sqrt{264}})^2=(\sqrt{a}+\sqrt{b})^2\)

\(17+\sqrt{264}=a + 2sqrt{ab}+b\)

And now we should try to express first part of equation in the form of second equation. As we have 2 before root in right side of equation, we should extract 2 from root in left side of equation:

\(\sqrt{264}=\sqrt{4 * 66}=2\sqrt{66}\)

And as a final step we should find roots for equations \(ab=66\) and \(a+b=17\) this is 6 and 11

And we can write our equation in symmetric view:

\(11+2\sqrt{11*6}+6=a + 2sqrt{ab}+b\)

\(a - b = 11 - 6 = 5\)

So answer is E

_________________

Simple way to always control time during the quant part.

How to solve main idea questions without full understanding of RC.

660 (Q48, V33) - unpleasant surprise

740 (Q50, V40, IR3) - anti-debrief