Which of the following is the correct ordering of \(2√13\), \(4√3\), \(5√2\) and \(3√6\) ?


A. \(2√13 < 3√6 < 5√2 < 4√3\)

B. \(3√6 < 5√2 < 4√3 < 2√13\)

C. \(4√3 < 5√2 < 2√13 < 3√6\)

D. \(5√2<4√3<3√6<2√13\)

E. \(2√13 < 3√6 < 4√3 < 5√2\)
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We can square each number:

(2√13)^2 = 4 x 13 = 52

(4√3)^2 = 16 x 3 = 48

(5√2)^2 = 25 x 2 = 50

(3√6)^2 = 9 x 6 = 54

Since 48 < 50 < 52 < 54, then we know that 4√3 < 5√2 < 2√13 < 3√6.

Answer: C
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Square all the numbers to get

\(2√13\), 52
\(4√3\), 48
\(5√2\) 50
\(3√6\) 54

Answer C
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