Squares and Roots I

$\frac { \sqrt { 2 } }{ 2 } =m$

$\frac { 2 }{ 4 } =\frac { 1 }{ 2 } ={ m }^{ 2 }$

$\sqrt { \frac { 1 }{ 2 } } ={ m }$

$\frac{\sqrt{2}}{2}=m$ $\frac{1}{\sqrt{2}}=m$ Which can be written as $m=\sqrt{\frac{1}{2}}$

$\frac { \sqrt { n } }{ n } =m\quad =>\quad \frac { 1 }{ \sqrt { n } } =m\\ Putting\quad \boxed { n=2 } \\ m=\frac { 1 }{ \sqrt { 2 } } \quad or\quad m=\sqrt { \frac { 1 }{ 2 } }$

According to question:

$\frac{\sqrt{n}}{n} = m, n=2$

$\frac{\sqrt{2}}{2} = m$

$\frac{\sqrt{2}}{\sqrt{2} \times \sqrt{2}} = m$

$\frac{1}{\sqrt{2}} = m$

$m = \sqrt{\frac{1}{2}}$

or

$\frac{1}{m} = \sqrt{n}, n=2$

$\frac{1}{m} = \sqrt{2}$

$m = \sqrt{\frac{1}{2}}$

Thus, $m = \boxed{\sqrt{\frac{1}{2}}}$

Given m=under root n/n that is under root 2/2 hence under root 1/underroot 2

1/m = Vn => 1/Vn=m => m=1/V2=V(1/2)

SqRT(n)/n=m implies,squaring on bothsides we get n/n^2=m^2 implies 1/m=n^(1/2)

Given m=under root n/n that is under root 2/2 hence under root 1/underroot 2 is ans.

K.K.GARG.India