Squares and Roots II

Algebra Level 1

Using following relation from the last problem :

$\frac { \sqrt { n } }{ n } =m\quad \Rightarrow \quad \frac { 1 }{ m } =\sqrt { n }$ ,

if m is $\sqrt { \frac { 1 }{ 3 } }$ , find n .

\sqrt { \frac { 2}{3 } }

4 3 5

4 solutions

Victor Paes Plinio
Apr 11, 2014

$\frac { \sqrt { n } }{ n } =\sqrt { \frac { 1 }{ 3 } }$

$\frac { n }{ { n }^{ 2 } } =\frac { 1 }{ 3 }$

${ n }^{ 2 }=3n$

$\frac { { n }^{ 2 } }{ n } =\frac { 3n }{ n }$

$n=3$

Nagendra Sistla
Apr 13, 2014

n=3

Kaveesh Dashora
Jan 18, 2015

$\frac { 1 }{ m } =\sqrt { n }$

$\frac { 1 }{ \sqrt { \frac { 1 }{ 3 } } } =\sqrt { n }$

squaring both sides

$\quad \frac { 1 }{ \frac { 1 }{ 3 } } = n\quad$

$n = 3$

Saurabh Mallik
Apr 26, 2014

According to question:

$\frac{\sqrt{n}}{n} = m, m=\sqrt{\frac{1}{3}}$

$\frac{\sqrt{n}}{n} = \sqrt{\frac{1}{3}}$

Squaring both sides:

$\frac{n}{n^{2}} = \frac{1}{3}$

${n^{2}} = 3n$

$\frac{n^{2}}{n} = \frac{3n}{n}$

$n = 3$

$\frac{1}{m} = \sqrt{n}, m=\sqrt{\frac{1}{3}}$

$\frac{1}{\sqrt{\frac{1}{3}}} = \sqrt{n}$

$\sqrt{3} = \sqrt{n}$

Squaring both sides:

$n = 3$

Thus, $n = \boxed{3}$