Question

What's the geometric mean between 3√5 and 6√5

Answer 1

3√10

Explanation:

`GM=\sqrt{(3√(5))(6√(5))}=√(18*5)=√(90)=3√(10)`

Answer 2

Answer:
`3√(10)`

Work Shown:

Part 1

`g = \text{geometric mean of x and y}\\\\g = \sqrt{\text{x}\text{y}}\\\\g = \sqrt{3√(5)*6√(5)}\\\\g = \sqrt{(3*6)*(√(5)*√(5))}\\\\g = \sqrt{18√(5*5)}\\\\g = \sqrt{18√(5^2)}\\\\g = √(18*5)\\\\g = √(90)\\\\`

Part 2

`g = √(90)\\\\g = √(9*10)\\\\g = √(9)*√(10)\\\\g = 3√(10)\\\\`