35√×2 √10
To simplify the expression 35√2 √10, first combine the square roots by multiplying the coefficients and the radicands:
35√2 √10 = 35 √(2*10) = 35 √(20)
Next, simplify the square root of 20:
√(20) = √(4*5) = √4 *√5 = 2√5
Therefore, 35√2 √10 simplifies to 35 * 2√5, or 70√5.
To simplify the expression 35√2 √10, we first multiply the coefficients (numbers outside the square root symbol), which are 35 and 2:
35 * 2 = 70
Next, we multiply the radicands (numbers inside the square root symbol), which are √2 and √10:
√2 * √10 = √(2 * 10) = √20
To simplify √20, we need to find the largest perfect square that is a factor of 20. In this case, 4 is the largest perfect square that divides evenly into 20:
√20 = √(4 * 5)
Now, we can separate the square root into two separate terms:
√(4 * 5) = √4 * √5
The square root of 4 is 2, so we can substitute that value:
√4 * √5 = 2 * √5
Finally, substituting this result back into the original expression, we have:
35√2 √10 = 70 * (2 * √5) = 140√5
Therefore, the simplified expression is 140√5.
To multiply the radicals √35 and √2√10, you can simplify each radical separately first and then multiply the results together. Here's how you can do it step by step:
Step 1: Simplify √35
The square root of 35 (√35) cannot be simplified further because 35 is not a perfect square. So, √35 remains the same.
Step 2: Simplify √2√10
To simplify the product of √2 and √10 (which can be written as √2 * √10), you can use the property of radicals that states √a * √b = √(a * b). Applying this property, you can combine the square roots of 2 and 10 into a single square root of their product, which is 2 * 10 = 20. Therefore, √2√10 simplifies to √20.
Step 3: Multiply the simplified radicals
Now that you have √35 and √20, you can multiply them: √35 * √20 = √(35 * 20). The product of 35 and 20 is 700, so the simplified expression becomes √700.
Step 4: Simplify √700
To simplify √700, you need to find the largest perfect square factor of 700. In this case, it is 100, because 10 * 10 = 100. You can write 700 as 100 * 7. Applying the property of radicals again, √(100 * 7) simplifies to √100 * √7, which is 10√7.
So, the final result of √35 * √2√10 is 10√7.