Which of the following statements is true?

Question

A.  3\sqrt{7}<2\sqrt{15}<\frac{5\sqrt{13}}{\sqrt{5}}<\frac{39}{5}

B.  2\sqrt{15}<\frac{39}{5}<3\sqrt{7}<\frac{5\sqrt{13}}{\sqrt{5}}

C.  2\sqrt{15}<3\sqrt{7}<\frac{39}{5}<\frac{5\sqrt{13}}{\sqrt{5}}

D.  2\sqrt{15}<3\sqrt{7}<\frac{5\sqrt{13}}{\sqrt{5}}<\frac{39}{5}

E.  2\sqrt{15}<\frac{5\sqrt{13}}{\sqrt{5}}<3\sqrt{7}<\frac{39}{5}

Lampard42 · Accepted Answer

Took 2 minutes to arrive at how to approach this problem. Here is my working

Convert all numbers to square roots that is a) 3\sqrt{7}  is  \sqrt{63} ; b)  2\sqrt{15}  is  \sqrt{60} ; c) \frac{5\sqrt{13}}{\sqrt{5}}  is  \sqrt{65}  d) 39/5 is  \sqrt{7.8^2}  is  \sqrt{60.8}  so IMO B

QuantMadeEasy · Answer

Squaring each term to remove square root and then compare the terms
 
(3√7)^2 = 9*7 = 63
(2√15)^2 = 4*15 = 60
(5√13/√5)^2 = 25*13/5 = 65
(39/5)^2 = 60.44

B is correct.

Kanika3agg · Answer

make a baseline for comparison -

a=3sqrt(7) = sqrt(63) 
b=2sqrt(15) = sqrt(60)
c=5sqrt(13)/sqrt(5) = sqrt(65)
d=39/5 less than 8 but almost equal to it

Then sorting answers in an order
we now know that 
b<a,d<c

we have to figure out the position of a and d.

Find out the value of a by long division method and the compare

b<d<a<c

Regor60 · Answer

Nothing quicker than what's been described in the previous responses

Posted from my mobile device

Kinshook · Answer

Asked: Which of the following statements is true?

A.  3\sqrt{7}<2\sqrt{15}<\frac{5\sqrt{13}}{\sqrt{5}}<\frac{39}{5} 
 \sqrt{63}<\sqrt{60}<\sqrt{65}<7.8 : FALSE

B.  2\sqrt{15}<\frac{39}{5}<3\sqrt{7}<\frac{5\sqrt{13}}{\sqrt{5}} 
 \sqrt{60}<7.8<\sqrt{63}<\sqrt{65} : TRUE

C.  2\sqrt{15}<3\sqrt{7}<\frac{39}{5}<\frac{5\sqrt{13}}{\sqrt{5}} 
  \sqrt{60}<\sqrt{63}<7.8<\sqrt{65}  : FALSE

D.  2\sqrt{15}<3\sqrt{7}<\frac{5\sqrt{13}}{\sqrt{5}}<\frac{39}{5} 
 \sqrt{60}<\sqrt{63}<\sqrt{65}<7.8  : FALSE

E.  2\sqrt{15}<\frac{5\sqrt{13}}{\sqrt{5}}<3\sqrt{7}<\frac{39}{5} 
 \sqrt{60}<sqrt{65}<\sqrt{63}<7.8}  : FALSE

IMO B

Gijmaja · Answer

just square them all and then they are easier to compare.

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Which of the following statements is true?

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Which of the following statements is true?

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