3√5 × 2√10
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To multiply these two numbers, we can first simplify each square root:
√5 = √(5) = √(5) × √(1) = √(5) × √(1) = √(5 × 1) = √(5) = √5
Similarly,
√10 = √(10) = √(10) × √(1) = √(10) × √(1) = √(10 × 1) = √(10) = √10
Now, we can multiply these simplified square roots:
√5 × √10 = √(5 × 10) = √(50) = √(25 × 2) = √25 × √2 = 5√2
Therefore, 3√5 × 2√10 = 3 × 2 × √5 × √10 = 6√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 coefficients (numbers in front of the square roots). In this case, multiply 3 by 2, which equals 6.
Step 2: Multiply the numbers inside the square roots. In this case, multiply 5 by 10, which equals 50.
Step 3: Combine the coefficients and the numbers inside the square roots. In this case, you will have 6√50, or simply 6√(2 × 25).
Step 4: Simplify the square root. Since 25 is a perfect square (5 × 5), you can take it out of the square root and leave it as plain 5. Therefore, the final answer is 6√2 × 5, or 30√2.
So, 3√5 × 2√10 equals 30√2.
To simplify the expression 3√5 × 2√10, we can multiply the numbers outside the square roots together and multiply the numbers inside the square roots together.
First, let's multiply the numbers outside the square roots:
3 × 2 = 6
Next, let's multiply the numbers inside the square roots:
√5 × √10 = √(5 × 10) = √50
Now, we have 6 times the square root of 50:
6√50
To simplify this further, we can find the factors of 50 and look for any perfect square factors:
The factors of 50 are 1, 2, 5, 10, 25, and 50.
We see that 25 is a perfect square.
So, we can rewrite the expression:
6√50 = 6√(25 × 2)
Since √25 = 5, we can simplify it even further:
6√(25 × 2) = 6 × 5√2
Finally, we can multiply the numbers outside the square root:
6 × 5 = 30
So, the simplified expression is 30√2.