Root 2

Since the square root of k is half the square root of 2, we can set up an equation like this and solve.

$\sqrt { k } =\quad \frac { \sqrt { 2 } }{ 2 } \\ { (\sqrt { k } ) }^{ 2 }=\quad { \left( \frac { \sqrt { 2 } }{ 2 } \right) }^{ 2 }\\ k=\frac { 2 }{ 4 } =.5$

Half of $\sqrt{2}$ is $\frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{(\sqrt{2})^2} = \frac{1}{\sqrt{2}} = \sqrt{\frac{1}{2}}$

Therefore $k = \frac{1}{2} = \boxed{0.5}$

We can write the problem as determining $k$ such that: $\dfrac12\sqrt{2}=\sqrt{k} \\\text{squaring both sides:} \Rightarrow k=\dfrac14\cdot2=\dfrac12=\boxed{0.5}$

$\frac{1}{2} \times \sqrt{2} = \frac{ \sqrt{2}}{2} = \frac{\sqrt{2}}{\sqrt{4}} = \sqrt{\frac{1}{2}}$ so k=0.5

here it is:

    √k =  √2/2

or, (√k)^2 = (√2/2)^2

or, k = 2/4=1/2=.5

$\sqrt(k)=\frac{\sqrt{2}}{2} \implies k=\frac{2}{4}=\frac{1}{2}=\boxed{\large{0.5}}$

1/2 or 0.5