Question

What is the geometric mean of 4√2 /19 and 6√2 / 19

Answer 1

`\large\boxed{(4\sqrt3)/(19)}`

Explanation:

`\text{Geometric mean of}\ x\ \text{and}\ y:\ √(xy)\\\\\text{We have}\ x=(4\sqrt2)/(19)\ \text{and}\ y=(6\sqrt2)/(19).\\\\\text{Substitute:}\\\\\sqrt{\left((4\sqrt2)/(19)\right)\left((6\sqrt2)/(19)\right)}=\sqrt{(24(\sqrt2)^2)/(19^2)}=\sqrt{((24)(2))/(19^2)}=(√(48))/(√(19^2))=(√((16)(3)))/(19)\\\\=(√(16)\cdot\sqrt3)/(19)=(4\sqrt3)/(19)`