A factory kept increasing its output by the same percentage every year. Find the percentage it is known that the output has doubled in the last two years.

To solve the problem, let us calculate the annual percentage increase in the factory's output, given that the output doubles in 2 years.

### Let the annual percentage increase be `r%` (expressed as a decimal `r/100`).

The factory's output increases geometrically because the percentage increase is the same every year. The relationship between the output after 2 years and the initial output can be expressed as:

Output after 2 years = (Output initially) × (1 + r/100)^2

It is given that the output doubles in 2 years. Thus:

2 = (1 + r/100)^2

### Step 1: Solve for `(1 + r/100)`

Taking the square root of both sides:

√2 = 1 + r/100

The approximate value of √2 is 1.414, so:

1.414 = 1 + r/100

### Step 2: Solve for `r`

r/100 = 1.414 - 1
r/100 = 0.414

Multiplying both sides by 100:

r = 41.4

### Final Answer:

The factory's output increases by **41.4% per year**.