Question

The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.

Options

• 1

• –1

• `2sqrt(2)`

• 3

Answer 1

The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is 1.

Explanation:

Mean proportion between x and y = `sqrt(xy)`

∴ Mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)`

= `sqrt((3 + 2sqrt(2))(3 - 2sqrt(2))`

= `sqrt(3^2 - (2sqrt(2))^2)`  ...[∵ (a + b)(a – b) = a² – b²]

= `sqrt(9 - 8)`

= `sqrt(1)`

= 1