show all of your steps for how to simplify 3sqare root of 5 x 2 square root of 10. answer in simplified radical form

Answer 1

To simplify the expression 3√5 × 2√10, follow these steps:

Step 1: Recognize that both terms have square roots, so we can apply the product property of square roots, which states that √(a) × √(b) = √(a × b).

Step 2: Apply the product property to the expression: 3√5 × 2√10 = (3 × 2)√(5 × 10).

Step 3: Simplify the expression within the square root: (3 × 2)√(5 × 10) = 6√(50).

Step 4: 50 can be simplified by factoring its square roots: 6√(50) = 6√(25 × 2).

Step 5: Simplify the expression within the square root: 6√(25 × 2) = 6√25 × √2.

Step 6: √25 is equal to 5: 6√25 × √2 = 6 × 5 × √2.

Step 7: Multiply the numbers outside the square root: 6 × 5 × √2 = 30√2.

The simplified radical form of 3√5 × 2√10 is 30√2.