radicals multiply and simplify by factoring
____ ______
^3|y^7* ^3|16y^8
unsure how to do root square sign.
I don't understand your symbols.
If I was going to take the square root of 25x^2y^4, I would write:
sqrt(25x^2y^4) = 5xy^2.
Name correctin.
To simplify and multiply radicals by factoring, you can use the following steps:
Step 1: Determine the prime factors of the numbers under the radicals.
In your question, the number under the first radical is y^7. Since it does not have any perfect cube factors, you can leave it as is.
The number under the second radical is 16y^8. To find its prime factors, you need to break it down into its constituent parts. First, factor out the perfect cube part, which is 2^3 (since 2 * 2 * 2 = 8). Then, you have (2^3)(y^8).
Step 2: Rewrite the expression using the prime factors.
So, we can rewrite the expression as follows:
√(y^7 * 16y^8) = √(y^7 * 2^3 * y^8)
Step 3: Pull out perfect cube factors from under the radical.
Since you are multiplying the factors, you can split the radical into two separate radicals:
√(y^7 * 2^3 * y^8) = √(y^7) * √(2^3 * y^8)
Step 4: Simplify the radicals.
√(y^7) is equivalent to y^(7/2) because the square root (√) represents the exponent of 1/2.
√(2^3 * y^8) is equivalent to 2 * y^(8/2) because 2^3 is 8 and y^8 is y^(8/2).
So, the simplified expression becomes:
y^(7/2) * 2 * y^(8/2)
Step 5: Combine the like terms.
To combine like terms with the same base, you add their exponents.
y^(7/2) * 2 * y^(8/2) = 2y^(7/2 + 8/2) = 2y^(15/2)
Therefore, the final simplified expression is 2y^(15/2).
Regarding the square root symbol (√), it can be represented as a caret (^) with the exponent 1/2. So, square root of a variable "x" can be written as x^(1/2).