Question

Which is the greatest out of the following ?

• A. $\sqrt[3]{31.728}$
• B. $\frac{\sqrt{3}-1}{\sqrt{3}+1}$
• C. ${\left(\frac{1}{2}\right)}^{-2}$
• D. $\frac{17}{8}$

Answer 1

The correct option is C ${\left(\frac{1}{2}\right)}^{-2}$

$\Rightarrow \sqrt[3]{31.728}=1.2$

$\Rightarrow \frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{(\sqrt{3}-1{)}^2}{(\sqrt{3}+1)(\sqrt{3}-1)}=\frac{3+1-2\sqrt{3}}{3-1}$

$=\frac{4-2\sqrt{3}}{2}=2-\sqrt{3}$

$=2-1.732=0.268$

$\Rightarrow {\left(\frac{1}{2}\right)}^{-2}=2^2=4$

$\Rightarrow \frac{17}{8}=2.2125$

$\therefore {\left(\frac{1}{2}\right)}^{-2}$ is the greatest.