Question

without using a calculator, choose the stament that best describes the value of the squareroot of 24?

Answer 1

Given the expression;

$\sqrt[\square]{24}$

Before we can determine the statement that best describe the expression, we need to first simplify and write it in surd format as shown;

$\begin{gathered} \sqrt[\square]{24}=\text{ }\sqrt[\square]{4\times6} \\ =\text{ }\sqrt[\square]{4}\times\sqrt[\square]{6} \\ =\text{ 2}\sqrt[\square]{6} \\ \end{gathered}$

Note that square root 6 is close to 2.5, hence;

$\begin{gathered} 2\sqrt[\square]{6}=2\times2.5 \\ 2\sqrt[\square]{6}\approx5.0 \end{gathered}$

This means that the statement squareroot of 24 is between 4.5 and 5 is correct since the the value is not greater than 5 and is more than 4.5. Option B is correct