Simplify: square root of 1/96 X square root of 3
Sqrt(1/96) =1/(4 sqrt(6))=1/(4 sqrt(2)*sqrt(3)) x sqrt(3)=sqrt(3)/[4 sqrt(2) sqrt(3)]. Cancel sqrt(3) and multiply by sqrt(2):
sqrt(2) / (4 x 2)=sqrt(2)/8.
\(\sqrt{\dfrac{1}{96}}\times \sqrt3\\ =\sqrt{\dfrac{3}{96}}\\ =\sqrt{\dfrac{1}{32}}\\ =\dfrac{\sqrt{1}}{\sqrt{32}}\\ =\dfrac{1}{4\sqrt{2}}\\ =\dfrac{1\times\sqrt2}{4\sqrt2 \times \sqrt2}\\ =\dfrac{\sqrt2}{8}\)
