Answer:
2[tex]\sqrt{10}[/tex]
Step-by-step explanation:
The geometric mean of a and b is
[tex]\sqrt{ab}[/tex]
Here a = 2[tex]\sqrt{8}[/tex] and b = 5[tex]\sqrt{2}[/tex], thus
ab = 2[tex]\sqrt{8}[/tex] × 5[tex]\sqrt{2}[/tex] = 10[tex]\sqrt{16}[/tex] = 10 × 4 = 40, then
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{40}[/tex] = [tex]\sqrt{4(10)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex] = 2[tex]\sqrt{10}[/tex]
