Show all of your steps for how to simplify 3√5×2√10
. Your final answer should be in simplified radical form (not a decimal).
To simplify the expression 3√5 × 2√10, we can first simplify the square roots separately and then multiply the simplifications together.
1. Simplify √5:
The square root of 5 cannot be simplified any further because 5 is not a perfect square.
2. Simplify √10:
The square root of 10 can be simplified by expressing it as the product of the square root of its largest perfect square factor. The largest perfect square factor of 10 is 2:
√10 = √(2 × 5) = √2 × √5 = √2√5
3. Multiply the simplified square roots together:
Now that both square roots are simplified, we can multiply them together:
3√5 × 2√10 = 3(√5) × 2(√2√5) = 6(√(5 × 2 × 5)) = 6(√(50)) = 6√50
4. Simplify the final answer:
The square root of 50 can be simplified by expressing it as the product of the square root of its largest perfect square factor. The largest perfect square factor of 50 is 25:
6√50 = 6√(25 × 2) = 6(√25√2) = 6(5√2) = 30√2
Therefore, the simplified form of 3√5 × 2√10 is 30√2.
To simplify the expression 3√5 × 2√10, follow these steps:
Step 1: Multiply the coefficients (the numbers outside the radical): 3 × 2 = 6.
Step 2: Multiply the numbers inside the radical: (√5) × (√10) = √(5 × 10) = √50.
Step 3: Simplify the square root of 50. We can break √50 down into its simplest form by finding the largest perfect square that divides into 50, which is 25. So we have √50 = √(25 × 2).
Step 4: Simplify the square root of 25 to 5, and bring the 2 out of the radical: 5 × 2√2 = 10√2.
Therefore, the simplified form of 3√5 × 2√10 is 10√2.
To simplify the expression 3√5 × 2√10, we can follow these steps:
Step 1: Multiply the coefficients (the numbers outside the square roots): 3 × 2 = 6.
Step 2: Multiply the numbers inside the square roots: √5 × √10 = √(5 × 10) = √50.
Step 3: Simplify the square root of 50:
- Notice that 50 can be factored into 2 × 25, and since 25 is a perfect square (5^2), we can simplify further.
- √50 = √(2 × 25) = √(2 × 5^2) = 5√2.
Step 4: Combine the coefficients and the simplified square root: 6 × 5√2 = 30√2.
Therefore, the simplified form of 3√5 × 2√10 is 30√2.