1. **State the problem:** Calculate the value of $\sqrt{50} \times 3$. 2. **Recall the formula and rules:** The square root of a number $a$ is a value that, when multiplied by itself, gives $a$. Also, multiplication is associative and commutative. 3. **Simplify the square root:** $$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$$ 4. **Multiply by 3:** $$3 \times 5\sqrt{2} = 15\sqrt{2}$$ 5. **Final answer:** $$15\sqrt{2}$$ This is the simplified exact form of the expression.