Compute the value of ((0.35)2 − (0.03)2) / 0.19 up to 3 decimal places:

Concept

The difference-of-squares identity rewrites a2 − b2 as (a − b)(a + b).

This factorization reduces two squaring operations to a product and makes decimal arithmetic easier to check.

Application

1. Let a = 0.35 and b = 0.03. Then the numerator is a2 − b2.

2. Apply the identity: a2 − b2 = (0.35 − 0.03)(0.35 + 0.03).

3. Compute the factors: 0.32 × 0.38 = 0.1216.

4. Divide by the denominator: 0.1216 ÷ 0.19 = 0.64.

Cross-check

Direct calculation gives 0.352 = 0.1225 and 0.032 = 0.0009; their difference is 0.1216, and 0.64 × 0.19 = 0.1216.

Therefore, the value up to three decimal places is 0.640.