1. **State the problem:** Simplify the expression $\sqrt{147}$.\n\n2. **Recall the formula and rules:** The square root of a product can be expressed as the product of the square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. We look for perfect square factors of 147 to simplify the root.\n\n3. **Factorize 147:**\n$$147 = 49 \times 3$$\nwhere 49 is a perfect square since $49 = 7^2$.\n\n4. **Apply the square root property:**\n$$\sqrt{147} = \sqrt{49 \times 3} = \sqrt{49} \times \sqrt{3}$$\n\n5. **Simplify the square root of the perfect square:**\n$$\sqrt{49} = 7$$\n\n6. **Write the simplified form:**\n$$\sqrt{147} = 7 \sqrt{3}$$\n\n**Final answer:** $\boxed{7 \sqrt{3}}$