Can one capital ship combine battleship protection with cruiser speed?

Did any design truly combine battleship-grade protection and firepower with cruiser speed and range?

Not completely; speed and range demand hull volume and machinery, so the cruiser role historically tended to produce a larger ship rather than a battleship with every advantage added.

No ship fully solved the four-way tradeoff. Cruisers needed machinery, fuel, and hull length for speed and range, which could make them physically larger than contemporary battleships even when their armour was lighter. Adding battleship protection and firepower to those requirements drives displacement upward rather than creating a cost-free hybrid. Ships such as Vanguard and New Jersey came close in some respects, but the answer remains a design compromise rather than a perfect combination. The exchange gives a compact explanation for why battlecruisers and fast battleships occupy a spectrum instead of one universally optimal type.