bmwhype2 wrote:
\(q = 3\sqrt{3}\)
\(r = 1 + 2\sqrt{3}\)
\(s = 3 + \sqrt{3}\)
If q, r and s are the numbers shown above, which of the following shows their order from greatest to least?
(A) q, r, s
(B) q, s, r
(C) r, q, s
(D) s, q, r
(E) s, r, q
is there a shortcut to this question besides substituting 1.7 into each equation and working it out?
Yes there is a shortcut or an alternate method.
\(q = 3\sqrt{3}\) write q as it is
\(r = 1 + 2\sqrt{3}\) . write this as \(1+\sqrt{3} +\sqrt{3}\)
\(s = 3 + \sqrt{3}\) write this as \( \sqrt{3}(\sqrt{3}+1)\)
so clearly observing the above trend we can see that
q is clearly the greatest.
and s>r since in this case multiplying \(\sqrt{3} \) to \(1+\sqrt{3}\) will yield a greater value than than adding .
hope this helps. Not exactly a shortcut but a method involving number sense.