1. First, multiply the coefficients which are the numbers in front of the square roots.3 times 2 equals 6.2. Next, multiply the radicands which are the numbers inside the square roots.The radicands are 5 and 10. So we multiply 5 times 10 to get 50.Therefore, √5 times √10 equals √50.3. Now, we combine our results from steps 1 and 2.This gives us 6√50.4. Next, we simplify √50. We can break down 50 into its factors.50 can be factored into 25 times 2.Since 25 is a perfect square, we know √50 equals √25 times √2.The square root of 25 is 5, so we have 5√2.5. Finally, we substitute back into the expression we had.Now we have 6 times 5√2 which equals 30√2.So, the final answer in simplest radical form is30√2. SImplify that
1 answer
The final result you've provided is already in simplest radical form: \(30\sqrt{2}\).
There are no further simplifications that can be made to this expression since the coefficient (30) and the radical (\(\sqrt{2}\)) cannot be simplified further together. Therefore, the simplest form is indeed:
\[ 30\sqrt{2} \]
If you need anything else or have other expressions to simplify, feel free to ask!
