Show all of your steps for how to simplify 3√5 x 2√10. Your final answer should be in simplified radical form (not a decimal). Answers only with no work shown will receive no credit
To simplify 3√5 x 2√10, we can start by multiplying the coefficients (numbers outside the square roots) and then multiplying the radicands (numbers inside the square roots).
Multiplying the coefficients:
3 x 2 = 6
Multiplying the radicands:
√5 x √10 = √(5 x 10) = √50
Now, let's simplify √50. We can break down 50 into its prime factors: 2 x 5 x 5.
√50 = √(2 x 5 x 5) = √(2 x 5^2) = √2 x √(5^2) = 5√2
Therefore, 3√5 x 2√10 simplifies to 6 x 5√2, or 30√2.