A square array of dimes contains 196 dimes.

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14^2 = 196, so ...

To find the number of dimes in a square array, you first need to determine the dimensions of the square array. Let's call the number of dimes on each side of the square "n".

The total number of dimes in the square array can be calculated by squaring the value of "n". In this case, we know that the total number of dimes is 196, so we can set up the equation:

n² = 196

To solve for "n", we need to find the square root of both sides of the equation:

√(n²) = √196

Since we are dealing with a square array, the square root of "n²" simplifies to just "n". The square root of 196 is 14, so:

n = 14

Now we know that the number of dimes on each side of the square array is 14. To find the total number of dimes, we can again use the formula for calculating the area of a square:

Total number of dimes = n² = 14² = 196

Therefore, there are 196 dimes in the square array.