Final answer:
To simplify √1256, break it down into prime factors and simplify the square root of the factors. The simplified expression is 2√314.
Step-by-step explanation:
To simplify the radical √1256, we can break it down into its prime factors. The factorization of 1256 is 2 × 2 × 2 × 157. Since the square root can be expressed as the product of the square roots of the factors, we can simplify it as 2√(2 × 157). Simplifying further, we have 2√314. Finally, we recognize that 314 is not a perfect square and cannot be simplified any further. Therefore, the simplified expression for √1256 is 2√314.
Learn more about Simplifying square roots