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