how do you multiply and simplify 3*^3sqrt of 5y^3* 2* ^3sqrt of 50y^4
To multiply and simplify the expression (3∛5y^3) * (2∛50y^4), we can follow these steps:
Step 1: Simplify the numbers inside the cube root.
- ∛5 can't be simplified further because 5 does not have a perfect cube factor.
- ∛50 can be simplified as follows:
∛50 = ∛(25 * 2) = ∛25 * ∛2 = 2∛2
So, we have:
(3∛5y^3) * (2∛50y^4) = 3 * 2 * (∛5 * 2∛2 * y^3 * y^4)
Step 2: Combine the coefficients (numbers in front).
3 * 2 = 6
Now we have:
6 * (∛5 * 2∛2 * y^3 * y^4)
Step 3: Simplify the variables.
y^3 * y^4 = y^(3+4) = y^7
We are left with:
6 * (∛5 * 2∛2 * y^7)
Step 4: Simplify the cube roots.
We can multiply the numbers outside the cube roots together and simplify them.
So, (∛5 * 2∛2) = 2 * ∛10
The expression becomes:
6 * (2 * ∛10 * y^7)
Step 5: Combine like terms by multiplying the integers:
6*2 = 12
Finally, we have:
12 * (∛10 * y^7)
The simplified expression is:
12∛10y^7