Question

What are like surds and unlike surds? Identify and write the set of like surds in the following groups:
a) { $\sqrt{8},\sqrt{12},\sqrt{20},\sqrt{54}$ }
b) { $\sqrt{50},\sqrt[3]{354},\sqrt[4]{432}$ }
c) {$\sqrt{8},\sqrt{18},\sqrt{32},\sqrt{50}$}.

Answer 1

Like Surds: Like surds are those surds which has same radicand.

Unlike surds: Unlike surds are those surds which has different radicand.

$a\left)\right\{\sqrt{8},\sqrt{12},\sqrt{20},\sqrt{54}\}$ can be written as $\{2\sqrt{2},2\sqrt{3},2\sqrt{5},3\sqrt{6}\}$-- since radicands are different so it is a set of unlike surds.

$b\left)\right\{\sqrt{50},\sqrt[3]{354},\sqrt[4]{432},\}$ can be written as $\{5\sqrt{2},3\sqrt{2},2\sqrt{2}\}$ --since radicands are same so it is a set of like surds.

$c\left)\right\{\sqrt{8},\sqrt{18},\sqrt{32},\sqrt{50}\}$ can be written as $\{2\sqrt{2},3\sqrt{2},4\sqrt{2},5\sqrt{2}\}$--since radicands are same so it is a set of like surds.