3sqrt5 multiply 2sqrt10
To multiply √5 by √10, we multiply the numbers outside (√5 and √10) and also multiply the numbers inside (5 and 10):
√5 * √10 = (√5)(√10) = √(5 * 10) = √50
To simplify √50, we can break it down into the product of two numbers where one of the numbers is a perfect square:
√50 = √(25 * 2) = √25 * √2 = 5√2
Therefore, 3√5 * 2√10 can be simplified to:
3√5 * 2√10 = 3 * 2 * √5 * √10 = 6 * √(5 * 10) = 6 * √50 = 6 * 5√2 = 30√2
To multiply 3√5 by 2√10, you can follow these steps:
Step 1: Multiply the numbers outside the square root:
3 * 2 = 6.
Step 2: Multiply the numbers inside the square root:
√5 * √10 = √(5 * 10) = √50.
Step 3: Simplify the square root:
√50 can be simplified by finding the largest perfect square that divides evenly into 50, which is 25:
√50 = √(25 * 2) = √25 * √2 = 5√2.
Step 4: Combine the results from steps 1 and 3:
6 * 5√2 = 30√2.
Therefore, 3√5 multiplied by 2√10 equals 30√2.
To multiply these two square roots, you can apply the property of multiplication of radicals which states that the product of two square roots is equal to the square root of the product of their radicands.
In this case, we have 3√5 multiplied by 2√10.
To find the product, follow these steps:
Step 1: Multiply the coefficients (numbers outside the square roots).
Multiply 3 and 2: 3 x 2 = 6.
Step 2: Multiply the radicands (numbers inside the square roots).
Multiply 5 and 10: 5 x 10 = 50.
Step 3: Combine the results from step 1 and step 2.
The product of 3√5 and 2√10 is 6√50.
However, for simplification purposes, we can simplify the square root of 50.
Step 4: Find the largest perfect square that divides 50 evenly. In this case, it is 25.
50 ÷ 25 = 2.
Step 5: Rewrite the square root of 50 as the product of the square root of the perfect square found in step 4, and the remaining number.
√50 = √(25 x 2) = √25 x √2 = 5√2.
Therefore, the simplified product of 3√5 and 2√10 is 6√50 = 6 x 5√2 = 30√2.