Question

$\text{The numbers}2\sqrt{5},\frac{\sqrt{5}}{2},(\sqrt{5}{)}^3,\&\frac{5}{\sqrt{5}}$$\text{arranged in ascending order is}$

• A. $\frac{\sqrt{5}}{2}<\frac{5}{\sqrt{5}}<2\sqrt{5}<(\sqrt{5}{)}^3$
• B. $\frac{5}{\sqrt{5}}<\frac{\sqrt{5}}{2}<2\sqrt{5}<(\sqrt{5}{)}^3$
• C. $\frac{\sqrt{5}}{2}<2\sqrt{5}<\frac{5}{\sqrt{5}}<(\sqrt{5}{)}^3$
• D. $\frac{\sqrt{5}}{2}<\frac{5}{\sqrt{5}}<(\sqrt{5}{)}^3<2\sqrt{5}$

Answer 1

The correct option is A $\frac{\sqrt{5}}{2}<\frac{5}{\sqrt{5}}<2\sqrt{5}<(\sqrt{5}{)}^3$

Given numbers :
$2\sqrt{5},\frac{\sqrt{5}}{2},(\sqrt{5}{)}^3=5\sqrt{5},\frac{5}{\sqrt{5}}=\sqrt{5}$

The ascending order is
$\frac{\sqrt{5}}{2}<\sqrt{5}<2\sqrt{5}<5\sqrt{5}\text{or}\frac{\sqrt{5}}{2}<\frac{5}{\sqrt{5}}<2\sqrt{5}<(\sqrt{5}{)}^3$