$\sqrt{50} \times \sqrt{98}$ is equal to

### Concept & Formula When multiplying square roots, you can combine the multiplicands under a single square root before calculating the final value. $$ \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} $$ ### Step-by-Step Solution * **Method 1: Factorization** * Simplify each surd by extracting perfect square factors: * $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$ * $\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}$ * Multiply the simplified terms: * $(5\sqrt{2}) \times (7\sqrt{2})$ * $= (5 \times 7) \times (\sqrt{2} \times \sqrt{2})$ * $= 35 \times 2 = 70$ ### Exam Strategy & Shortcut Instead of breaking the numbers down, immediately combine them under one root and look for trailing zeros. $\sqrt{50 \times 98} = \sqrt{4900}$ Since $49 = 7^2$ and $100 = 10^2$, the square root of $4900$ is instantly recognizable as $70$. This skips the intermediate factorization entirely. ### Common Pitfall Students sometimes try to calculate the approximate decimal value of $\sqrt{50}$ (around $7.07$) and $\sqrt{98}$ (around $9.89$) and multiply them. This wastes significant time and introduces rounding errors that might make you pick a distractor option like 70.25. Always simplify algebraically first. ### Final Answer **Therefore, the correct answer is 70.**