simplify 3√5 *2 radical 10 make it simplified radical form
To simplify this expression, we need to simplify both radicals separately.
Starting with 3√5:
Since √5 cannot be simplified further, we'll leave it as is.
Next, let's simplify 2√10:
We can simplify the square root of 10 by factoring it into its prime factors: 2 * 5.
Thus, we have 2√(2 * 5), which simplifies to 2√2√5.
Now, let's combine the two radicals together:
3√5 * 2√2√5
Multiplying the coefficients:
3 * 2 = 6
Multiplying the two radical terms:
√5 * √2 = √(5 * 2) = √10
Therefore, the simplified expression is 6√10.
your step by step was pretty confusing can you please tell me how to simplfy
Certainly! Here's a step-by-step guide on how to simplify the expression 3√5 * 2√10:
Step 1: Simplify the first radical, 3√5, as it cannot be simplified further.
Step 2: Simplify the second radical, 2√10. We can simplify the square root of 10 by factoring it into its prime factors: 2 * 5. This gives us 2√(2 * 5), which can be further simplified to 2√2√5.
Step 3: Combine the simplified radicals from Step 1 and Step 2. This gives us 3√5 * 2√2√5.
Step 4: Multiply the coefficients (numbers in front of the radicals): 3 * 2 = 6.
Step 5: Multiply the two radical terms (√5 * √2 = √(5 * 2) = √10).
Step 6: Combine the coefficient from Step 4 and the simplified radical from Step 5. This gives us 6√10.
Therefore, the simplified form of 3√5 * 2√10 is 6√10.
To simplify the expression 3√5 * 2√10, we can start by simplifying each radical separately.
First, let's simplify the radical inside the square root (√10). We can find the prime factorization of 10, which is 2 * 5.
√10 = √(2 * 5) = √2 * √5
Now, let's simplify the expression before the multiplication:
3√5 * 2√10 = 3 * 2 * √5 * √2
Next, we can multiply the coefficients outside the radicals, which gives us:
3 * 2 = 6
Now, let's multiply the square roots together:
√5 * √2 = √(5 * 2) = √10
Finally, we can combine both results to simplify the expression:
3√5 * 2√10 = 6√10
Therefore, the simplified radical form of 3√5 * 2√10 is 6√10.