1. **Problem statement:** For the number 252, find the smallest whole number to multiply it by to get a perfect square, then find the square root of that perfect square. 2. **Step 1: Prime factorize 252.** $$252 = 2^2 \times 3^2 \times 7$$ 3. **Step 2: Identify factors with odd powers.** The factor 7 has an odd power (1). 4. **Step 3: Multiply by the smallest number to make all powers even.** Multiply by 7 to get: $$252 \times 7 = 2^2 \times 3^2 \times 7^2 = 1764$$ 5. **Step 4: Find the square root of the perfect square.** $$\sqrt{1764} = 42$$ --- **Final answer:** The smallest whole number to multiply 252 by is 7, and the square root of the resulting perfect square 1764 is 42.