Compare Your Answers
Completion requirements
Compare and order the following radicals from smallest to largest, without using a calculator.
\(-2\sqrt{6}, -\sqrt{50}, -6, -3\sqrt{7}, -4\sqrt{2}\)
\(-2\sqrt{6}, -\sqrt{50}, -6, -3\sqrt{7}, -4\sqrt{2}\)
Convert each number to an entire radical.
\( -2\sqrt 6 = -\sqrt {2^2 \cdot 6} = -\sqrt {24} \)
\(-\sqrt{50}\)
\(-6 = -\sqrt{6^2} = -\sqrt{36} \)
\(-3\sqrt{7} = -\sqrt{3^2\cdot 7} = -\sqrt{63} \)
\(-4\sqrt{2} = -\sqrt{4^2\cdot 2} = -\sqrt{32} \)
Notice that these radicals are all negative, so from smallest to largest they are
\(-\sqrt{63}, -\sqrt{50}, -\sqrt{36}, -\sqrt{32}, -\sqrt{24} \)
or
\(-3\sqrt{7}, -\sqrt{50}, -6, -4\sqrt{2}, -2\sqrt{6} \) (The preferred answer)
\( -2\sqrt 6 = -\sqrt {2^2 \cdot 6} = -\sqrt {24} \)
\(-\sqrt{50}\)
\(-6 = -\sqrt{6^2} = -\sqrt{36} \)
\(-3\sqrt{7} = -\sqrt{3^2\cdot 7} = -\sqrt{63} \)
\(-4\sqrt{2} = -\sqrt{4^2\cdot 2} = -\sqrt{32} \)
Notice that these radicals are all negative, so from smallest to largest they are
\(-\sqrt{63}, -\sqrt{50}, -\sqrt{36}, -\sqrt{32}, -\sqrt{24} \)
or
\(-3\sqrt{7}, -\sqrt{50}, -6, -4\sqrt{2}, -2\sqrt{6} \) (The preferred answer)
| For further information about converting between mixed and entire radicals, see pp. 274 – 276 of Pre-Calculus 11. |