1. The problem is to find the square root of 224. 2. We start by expressing 224 as a product of its prime factors. 3. Factorize 224: $$224 = 2 \times 112 = 2 \times 2 \times 56 = 2^3 \times 28 = 2^4 \times 14 = 2^5 \times 7$$ 4. So, $$224 = 2^5 \times 7$$. 5. The square root of a product is the product of the square roots: $$\sqrt{224} = \sqrt{2^5 \times 7} = \sqrt{2^5} \times \sqrt{7}$$. 6. Simplify $$\sqrt{2^5} = \sqrt{2^4 \times 2} = \sqrt{2^4} \times \sqrt{2} = 2^2 \times \sqrt{2} = 4\sqrt{2}$$. 7. Therefore, $$\sqrt{224} = 4\sqrt{2} \times \sqrt{7} = 4\sqrt{14}$$. 8. The simplified form of the square root of 224 is $$4\sqrt{14}$$. Final answer: $$\boxed{4\sqrt{14}}$$