Algebra
# Radical Expressions and Equations

If half of $\sqrt{2}$ is $\sqrt{k}$, then what is the value of $k?$

$\large \sqrt{\frac{1}{\sqrt{ x}}}=3, \ \ \ x = \ ?$

$\large \frac{\sqrt{12}-\sqrt{27}}{6}\times\sqrt{3}\times\sqrt{4}= \ ?$

$\large\color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} + \color{#20A900} 6^{\color{#3D99F6} 6} = \color{#20A900}6^ {\color{#624F41}a}$

If $\color{#624F41} a$ satisfies the equation above, what is the value of $\color{#624F41} a$?