Show all of your steps for how to simplify 3√5 x 2√10

Question

. Your final answer should be in simplest radical form (not a decimal).

Answer 1

To simplify the expression \( 3\sqrt{5} \times 2\sqrt{10} \), we can follow these steps:

1. Multiply the coefficients: Multiply the numbers outside the radicals. \[ 3 \times 2 = 6 \]

2. Multiply the radicals: Multiply the expressions inside the square roots. \[ \sqrt{5} \times \sqrt{10} = \sqrt{5 \times 10} = \sqrt{50} \]

3. Combine the results: Now we can combine the coefficient and the radical. \[ 6\sqrt{50} \]

4. Simplify the radical: Now we simplify \(\sqrt{50}\). We can factor \(50\) into \(25 \times 2\). \[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

5. Substituting back into the expression: \[ 6\sqrt{50} = 6 \times 5\sqrt{2} = 30\sqrt{2} \]

Thus, the final answer in simplest radical form is: \[ \boxed{30\sqrt{2}} \]