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 first multiply the coefficients (numbers outside the square roots) together: 3 x 2 = 6.
Next, we can multiply the numbers inside the square roots together: √5 x √10 = √(5 x 10) = √50.
Now, we need to simplify √50. We can find the largest perfect square that is a factor of 50, which is 25.
Thus, √50 = √(25 x 2) = √25 x √2 = 5√2.
Finally, we can combine the multiplied coefficients (6) with the simplified square root (5√2): 6 x 5√2 = 30√2.
Therefore, the simplified form of 3√5 x 2√10 is 30√2.