Find the square root of (272)2 − (128)2.

For any two numbers a and b, the difference of their squares factors as a2 − b2 = (a + b)(a − b). This lets you rewrite a difference of squares as a product of the sum and the difference of the two numbers, which is often much easier to compute than squaring directly.

1. Identify a = 272 and b = 128.

2. Compute the sum: a + b = 272 + 128 = 400.

3. Compute the difference: a − b = 272 − 128 = 144.

4. Apply the identity: a2 − b2 = (a + b) × (a − b) = 400 × 144 = 57600.

5. Take the square root: √57600 = √(400 × 144) = √400 × √144 = 20 × 12 = 240.

Cross-check by direct computation: 2722 = 73984 and 1282 = 16384, so 2722 − 1282 = 73984 − 16384 = 57600, and √57600 = 240 — confirming the identity-based result.