Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Question: Of the following, which is the best approximation of $$\sqrt{1.5}(266)^{3/2}$$

$$(A)~1,000~~~~(B)~2,700~~~~(C)~3,200~~~~(D)~4,100~~~~(E)~5,300$$

I used $1.5\approx1.44=1.2^2$ and $266\approx256=16^2$. Therefore the approximation by me is $4096$, so I chose $(D)$ which is wrong. The correct answer is $(E)$.

How should I find it out?

share|improve this question
    
Use Newtons Method. –  Damien Aug 18 '11 at 3:05
1  
This is the same question as this one. –  Jack Aug 18 '11 at 3:25

3 Answers 3

up vote 5 down vote accepted

$$\sqrt{1.5}\cdot266^{3/2}\approx1.2 \times 16^3 = 4915.2$$

The closest answer is (E) 5300. Great intuition on how to find simple approximations, but you forgot to multiply by $1.2$! Also note that $1.44<1.5$ and $256<266$, so you know the true answer must be above the discovered approximation, leaving only the last answer.

share|improve this answer
    
Okay, this is embarrassing ... I did the calculation wrong. Sorry bothering you guys, this question is simpler than I thought. –  Voldemort Aug 18 '11 at 3:42

$$\sqrt{\frac{3}{2}} \cdot ( \sqrt{266})^3 =\sqrt{\frac{3\cdot 266}{2}}\cdot (\sqrt{266})^2 = \sqrt{399} \cdot 266 \approx 266 \cdot 20 = 5320$$

This is closest to option (E)

Edit: Note that the only approximation I used here is $\sqrt{399}\approx \sqrt{400}$ so the result will differ by a factor of $\frac{\sqrt{399}}{20}$. This can be quickly approximated too, $\frac{\sqrt{399}}{20} = \sqrt{1-1/400} \approx 1 - 1/800 =0.9987 $.

share|improve this answer
    
Great solution! But I think my original answer is more intuitive. It is my calculation that went wrong, I forgot to multiply 1.2. –  Voldemort Aug 18 '11 at 3:45
    
@Voldemort: I favor pulling all the squares out of the radical first, just as kuch nahi did. I see nothing unintuitive about it. –  robjohn Aug 18 '11 at 4:21

$$\sqrt{1.5}(266)^{3/2} \approx \sqrt{\frac{16}{9}}(256)^{3/2} \approx \frac{4}{3} \times 4096 \approx 5460 $$

Hence, $(E)$

N.B. kuch nahi's answer is probably the "right" one ; this seemed more intuitive to me since I didn't need to compute $16^3$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.