Could you please help me with some math problems? Thanks!
Add or subtract terms wherever possible.
1. 2 cube root of 135 + cube root of 455
2.y cube root of 24 - cube root of 192xy^3
none of your numbers in the cube roots in either question can be "broken down" to produce like terms, so you cannot add or subtract them
eg. cuberoot(455) = cuberoot((5)(7)(13))
which gets you nowhere.
Sure! In both of these math problems, we are given cube roots of numbers. To add or subtract these terms, we need to find any like terms that can be combined.
Let's start with the first problem:
1. 2 cube root of 135 + cube root of 455
To check if we can simplify the cube roots to get like terms, we can try to factorize the numbers under the cube roots.
For the first term: Cuberoot(135)
We can factorize 135 as 3 * 3 * 3 * 5 = 3^3 * 5.
So, the first term becomes 2 * cuberoot(3^3 * 5).
For the second term: Cube root of 455
We find that 455 is not a perfect cube, and we cannot break it down any further.
Since the factorization of the second term does not match the first term, we cannot combine them. So, our final answer is:
2 cube root of 135 + cube root of 455
Now, let's move on to the second problem:
2. y cube root of 24 - cube root of 192xy^3
Again, we need to check if we can simplify the cube roots to get like terms.
For the first term: y cube root of 24
We try to factorize 24 as 2 * 2 * 2 * 3 = 2^3 * 3.
So, the first term becomes y * cuberoot(2^3 * 3).
For the second term: Cube root of 192xy^3
We find that 192 can be factorized as 2 * 2 * 2 * 2 * 2 * 2 * 3 = 2^6 * 3.
In this case, we also have the variable "y" raised to the power of 3, so we have y^3 * cuberoot(2^6 * 3).
Now, we compare the factorization of the first term with the second term. We see that both terms have a factor of 2^3 * 3, which means they are like terms.
So, we can combine the two terms:
y cube root of 24 - cube root of 192xy^3
= y * cuberoot(2^3 * 3) - y^3 * cuberoot(2^6 * 3)
= y * cuberoot(8 * 3) - y^3 * cuberoot(64 * 3)
= 2y * cuberoot(3) - 4y^3 * cuberoot(3)
Therefore, our final answer is:
2y cuberoot(3) - 4y^3 cuberoot(3)
I hope this helps! Let me know if you have any more questions.