Question

Which of the following is equivalent to the expression below? 196 - 54 +24 O A. 5/6 O B. 5 C. 36 D. 9/6

Answer 1

`\begin{gathered} \text{The equivalent expression is 3}\sqrt[]{6} \\ 3\sqrt[]{6} \end{gathered}`

OPTION C

Explanation

Given expression

`\sqrt[]{96}\text{ - }\sqrt[]{54}+\text{ }\sqrt[]{24}`

According to the law of surds,

`\sqrt[]{A\text{ }*\text{ B}}\text{ = }\sqrt[]{A}*\sqrt[]{B}`

The next step is to simplify the surds separately

`\begin{gathered} \sqrt[]{96}\text{ can be expr}essed\text{ as} \\ \sqrt[]{96}=\sqrt[]{16}*\sqrt[]{6} \\ \text{recall that, }\sqrt[]{16}\text{ = 4} \\ \sqrt[]{96}\text{ = 4}\sqrt[]{6} \\ \\ \sqrt[]{54} \\ \sqrt[]{54}\text{ = }\sqrt[]{9}\text{ }*\text{ }\sqrt[]{6} \\ \text{recall that, }\sqrt[]{9}\text{ = 3} \\ \sqrt[]{54}\text{ = 3}\sqrt[]{6} \\ \\ \sqrt[]{24} \\ \sqrt[]{24}\text{ =}\sqrt[]{4}\text{ }*\text{ }\sqrt[]{6} \\ \text{recall that, }\sqrt[]{4}\text{ = 2} \\ \sqrt[]{24}\text{ = 2}\sqrt[]{6} \end{gathered}`

The next step is to simplify the expression

`\begin{gathered} 4\sqrt[]{6}\text{ - 3}\sqrt[]{6}\text{ + 2}\sqrt[]{6} \\ \text{factor out }\sqrt[]{6} \\ =\sqrt[]{6}(4\text{ - 3 + 2)} \\ =\sqrt[]{6}\text{ (1 + 2)} \\ =\sqrt[]{6}\text{ (3)} \\ 3\sqrt[]{6} \end{gathered}`