Question

The surds $\sqrt{2},(3{)}^{1/3}$ and $(5{)}^{1/5},$ in their descending order are

• A. ${}^3\sqrt{3}$,${}^5\sqrt{5}$,$\sqrt{2}$
• B. $\sqrt{2}$,${}^3\sqrt{3}$,${}^5\sqrt{5}$
• C. $\sqrt{2}$,${}^5\sqrt{5}$,${}^3\sqrt{3}$,
• D. ${}^3\sqrt{3}$,$\sqrt{2}$,${}^5\sqrt{5}$

Answer 1

The correct option is D ${}^3\sqrt{3}$,$\sqrt{2}$,${}^5\sqrt{5}$

We have,

$a=\sqrt{2}$

$\log a=\frac{1}{2}\log 2=\frac{0.301}{2}=0.1501$

Since,

$b=(3{)}^{1/3}$

$\log b=\frac{1}{3}\log 3=\frac{0.477}{3}=0.155$

Since,

$c=(5{)}^{1/5}$

$\log c=\frac{1}{5}\log 5=\frac{0.699}{3}=0.139$

Therefore, the descending order

$(3{)}^{1/3},\sqrt{2},(5{)}^{1/5}$

Hence, this is the answer.