Quite a neat quick answer you did . I wrote √1.5 as √3/√2 . I then wrote 266 in prime factors 266=(2 x 7 x19), then distributed the exponential 3/2 to each term and then split each term, for instance 2^3/2 becomes 2 x 2^½. Did the same with the other terms. Multiplied all the integer terms to get 266, put all √terms together to get √401 End up with ≈ 266 x 20, hence 5320 and E. Yours was quicker.
My line of thought with out anything [ pen/paper/writing ]. Step 1. (266) ^ 3/2 = (sqrt(266))^3 ~= (16.2)^3 ~= 256*16.2 ~= 4000+ (definitely). Call this result p. Step 2. p * sqrt(1.5) ~= 1.35ish * p ~= 1.35 * (>4000) ~= 5.2 or 5.3K. Answer is 5300.
4096*1.2 is in fact 4915.2, so your approach doesn't quite work at the end, but it's still clearly more than 4100, so that's good enough given the multiple-choice answers.
My strategy: square everything. Calculate 1.5 × 266³ and figure out which answer squared is closest. (I got answer A because I completely messed up my calculations. ;-) )
![Lp. Сердце Вселенной #60 РОЖДЕНИЕ ЛОЛОЛОШКИ [Финал] • Майнкрафт](http://i.ytimg.com/vi/YoR0pAV9FVQ/mqdefault.jpg)
Quite a neat quick answer you did . I wrote √1.5 as √3/√2 .
I then wrote 266 in prime factors 266=(2 x 7 x19), then distributed the exponential 3/2 to each term and then split each term, for instance 2^3/2 becomes 2 x 2^½.
Did the same with the other terms. Multiplied all the integer terms to get 266, put all √terms together to get √401
End up with ≈ 266 x 20, hence 5320 and E. Yours was quicker.
My line of thought with out anything [ pen/paper/writing ].
Step 1. (266) ^ 3/2 = (sqrt(266))^3 ~= (16.2)^3 ~= 256*16.2 ~= 4000+ (definitely). Call this result p.
Step 2. p * sqrt(1.5) ~= 1.35ish * p ~= 1.35 * (>4000) ~= 5.2 or 5.3K.
Answer is 5300.
4096*1.2 is in fact 4915.2, so your approach doesn't quite work at the end, but it's still clearly more than 4100, so that's good enough given the multiple-choice answers.
Sometimes good enough is good enough haha!
My strategy: square everything. Calculate 1.5 × 266³ and figure out which answer squared is closest. (I got answer A because I completely messed up my calculations. ;-) )
1.5^0.5*(266)^(3/2)=266*(1.5*266)^.5=266*(3*133)^.5=266*(399)^0.5
That happens to me far too often in my videos, no shame in making mistakes if you use them as motivation to keep sharper.
Simplifies to 266 * sqrt(1.5 * 266), which is 266 * sqrt(399) giving about 266 * 20; so (E).