1. The problem asks to evaluate the square roots and products given: $$\sqrt{4} \times \sqrt{100} = 20$$ $$\sqrt{9} \times \sqrt{100} = 30$$ $$\sqrt{3969} = ?$$ 2. Recall the property of square roots: $$\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$$. 3. For the first two lines, the calculations are: - $$\sqrt{4} = 2$$ and $$\sqrt{100} = 10$$, so $$2 \times 10 = 20$$. - $$\sqrt{9} = 3$$ and $$\sqrt{100} = 10$$, so $$3 \times 10 = 30$$. 4. Now, to find $$\sqrt{3969}$$, we look for a number which squared equals 3969. 5. By prime factorization or estimation, $$63 \times 63 = 3969$$. 6. Therefore, $$\sqrt{3969} = 63$$. Final answer: $$\boxed{63}$$