simplify
√(x^5y^8)
the answer is
x^5/2y^4
does it matter if 5/2 is replaced with 2.5?
x^2.5y^4
its the same thing right?
Correct!
I would leave the 5/2 as a fraction.
To simplify the expression √(x^5y^8), we need to apply the rules of simplifying square roots. In this case, we can break down the expression inside the square root into factors raised to powers.
First, let's separate the expression into two parts: the factors with even powers and the factors with odd powers. In this case, the factors with even powers are y^8, which can be written as (y^4)^2, and the factors with odd powers are x^5.
Now, we can simplify the expression as follows:
√(x^5y^8) = √(x^5(y^4)^2)
Using the product rule of square roots, we can bring out the even powers outside the square root:
√(x^5(y^4)^2) = √x^5 * √(y^4)^2
Since the square root of x^5 is x^(5/2) and the square root of (y^4)^2 is y^4, we can simplify further:
√x^5 * √(y^4)^2 = x^(5/2) * y^4
Now, to address your question, x^(5/2) is not the same as x^2.5. The exponent 5/2 represents the square root of x^5, which is different from multiplying x by 2.5. Therefore, x^(5/2) and x^2.5 are not equivalent.
So, the correct simplified expression is x^(5/2) * y^4, or if you prefer a decimal approximation, you can use x^2.5 * y^4.