1. The problem is to find the square root of 1225. 2. Recall that the square root of a number $x$, denoted $\sqrt{x}$, is a value that when multiplied by itself gives $x$. 3. We look for a number $n$ such that $n^2 = 1225$. 4. Factorize 1225 into prime factors to simplify finding the root: $$1225 = 25 \times 49$$ 5. Recognize both 25 and 49 are perfect squares: $$\sqrt{25} = 5 \quad \text{and} \quad \sqrt{49} = 7$$ 6. Use the property of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, so $$\sqrt{1225} = \sqrt{25 \times 49} = \sqrt{25} \times \sqrt{49} = 5 \times 7 = 35$$ 7. Therefore, the square root of 1225 is 35.