Property 11
Ordering in Radical Expressions
If the power of the radicals are equal, the order is made with respect to increasing order. If the power of the radicals are not equal the order is made with respect to the same equality.
\(\blacksquare\quad a>b>c>0\)
\(\sqrt[m]{a}>\sqrt[m]{b}>\sqrt[m]{c}\)
Write the following radicals in increasing order.
1.
\(a=\sqrt5\)
\(b=\sqrt8\)
\(c=\sqrt6\)
2.
\(a=\sqrt[3]{12}\)
\(b=\sqrt[3]{17}\)
\(c=\sqrt[3]7\)
3.
\(x=\sqrt2\)
\(y=\sqrt[3]3\)
\(z=\sqrt[4]5\)
4.
\(a=3\sqrt5\)
\(b=4\sqrt2\)
\(c=2\sqrt{11}\)
5.
\(x=\sqrt3\)
\(y=\sqrt[3]5\)
\(z=\sqrt[6]{13}\)
6.
\(0<a<1\)
\(x=\sqrt a\)
\(y=\sqrt[3] a\)
\(z=\sqrt[6] a\)
7.
\(x=-3\sqrt5\)
\(y=-2\sqrt6\)
\(z=-4\sqrt2\)
8.
\(a=\samefrac1{\sqrt[3]{10}}\)
\(b=\samefrac1{\sqrt6}\)
\(c=\samefrac1{\sqrt[6]{75}}\)
9.
\(x=-\samefrac1{\sqrt{10}}\)
\(y=-\samefrac1{\sqrt{15}}\)
\(z=-\samefrac1{\sqrt6}\)