Question

The greatest number among $\sqrt[3]{32},\sqrt{3},\sqrt[3]{35}$ and $1.5$ is

• A. $\sqrt[3]{32}$
• B. $\sqrt{3}$
• C. $\sqrt[3]{35}$
• D. $1.5$

Answer 1

The correct option is B $\sqrt{3}$

LCM of $3,2=6$
Given numbers are $\sqrt[3]{32},\sqrt{3},\sqrt[3]{35},1.5$ i.e,
$2^{1/3},3^{1/2},5^{1/3},1.5$
$\therefore$ Raising each number to power $6$, we get
$(2^{1/3}{)}^6,(3^{1/2}{)}^6,(5^{1/3}{)}^6,(1.5{)}^6$

$=2^2,3^3,5^2,{\left(\frac{3}{2}\right)}^6$

$=4,27,25,\frac{729}{64}$
Of all these numbers, $27$ is the greatest.

$\Rightarrow \sqrt{3}$ is the greatest.