Please show the steps and explain how to do this as well.
3√8 · 2√5
3 sqrt ( 8 ) * 2 sqrt ( 5 ) =
3 * 2 * sqrt ( 8 ) * sqrt ( 5 ) =
6 sqrt ( 8 * 5 ) =
6 sqrt ( 40 ) =
6 sqrt ( 4 * 10 ) =
6 sqrt ( 4 ) * sqrt ( 10 ) =
6 * 2 * sqrt ( 10 ) =
12 sqrt ( 10 )
thank you so much :)
To simplify the expression 3√8· 2√5, follow these steps:
Step 1: Use the product property of radicals
According to the product property of radicals, the product of two radicals with the same radical sign √a * √b = √(a * b). Apply this property to the given expression:
3√8 · 2√5 = √(3 * 8) · √(2 * 5)
Step 2: Simplify the numbers inside the radicals
Evaluate the products inside the radicals:
√(3 * 8) · √(2 * 5) = √24 · √10
Step 3: Simplify the radicands
Reduce the radicands to their simplest forms. To do this, break each radicand into its prime factors:
√(24) = √(3 * 2^3) = 2√3
√(10) = √(2 * 5) = √(2) * √(5) = √2√5
Step 4: Combine the simplified radicands
Combine the simplified radicands:
2√3 · √2√5 = 2√6√5
Step 5: Apply the product property of radicals again, if needed
If there are multiple radical signs in a term, use the product property of radicals to combine them. In this case, we have √6√5, so we can combine them as follows:
2√6√5 = 2√(6 * 5) = 2√30
Therefore, the simplified expression is 2√30.