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If a, b and c have the values shown, which of the following shows thei [#permalink]
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Bunuel wrote:
\(a = \sqrt{2} + \sqrt{6}\)

\(b= \sqrt{3} + \sqrt{5}\)

\(c= 4\)

If a, b and c have the values shown, which of the following shows their order from least to greatest?


(A) a, b, c
(B) b, c, a
(C) b, a, c
(D) c, a, b
(E) c, b, a


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Even if we cannot recall the value of \(\sqrt{2}\) or \(\sqrt{3}\) or \(\sqrt{5}\)

As long as we keep \(\sqrt{6} > \sqrt{5} > \sqrt{3} > \sqrt{2}\) we can take approximate values keeping in mind \(\sqrt{4} = 2\) , \(\sqrt{9} =3\) as reference points.


\(\sqrt{2} = 1.2 \)( Purposefully taking a value different from the actual value ) I know it has to be more than \(1 \) but less than \(2 \)

\(\sqrt{3} = 1.5\) ( Purposefully taking a value different from the actual value ) I know it has be more than what value we have taken for \(\sqrt{2} = 1.2 \) but less than \(2\)

\(\sqrt{5} = 2.3\) ( Purposefully taking a value different from the actual value ) I know it has to be more than \(2 \) but less than \(3 \)

\(\sqrt{6}\) = a value more than \(\sqrt{5}\) but less than \(3\) hence let us take it as \(2.5\)


\( a = \sqrt{2} + \sqrt{6} = 1.2 + 2.5 = 3.7 \)

\( b= \sqrt{3} + \sqrt{5} = 1.5 +2.3 = 3.8\)

\(c = 4 \)

\(a < b < c\)

Ans A

Hope it's clear.
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Re: If a, b and c have the values shown, which of the following shows thei [#permalink]
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Bunuel wrote:
\(a = \sqrt{2} + \sqrt{6}\)

\(b= \sqrt{3} + \sqrt{5}\)

\(c= 4\)

If a, b and c have the values shown, which of the following shows their order from least to greatest?

(A) a, b, c
(B) b, c, a
(C) b, a, c
(D) c, a, b
(E) c, b, a


The three numbers (a, b, and c) are positive, so their ascending order must follow the ascending order of their squares.

a^2 = 2 + 2√12 + 6 = 8 + √48

b^2 = 3 + 2√15 + 5 = 8 + √60

c^2 = 16 = 8 + 8 = 8 + √64

Since a^2 < b^2 < c^2, we have:

a < b < c

Answer: A
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Re: If a, b and c have the values shown, which of the following shows thei [#permalink]
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