If y > 0, then ##\ y=\sqrt{y^2}\ .\ ## Right ?Marcin H said:Homework Statement
I just had a simplification question. How is (sqrt(xy))/y the same thing as sqrt(x/y)??
Homework Equations
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The Attempt at a Solution
I don't see how you can get that. I tried square rooting the top and bottom, but I don't think that gets you anywhere...
The purpose of simplifying "Sqrt(xy)/y" is to make the expression easier to work with and understand. Simplification involves reducing the expression to its most basic form by combining like terms and eliminating unnecessary components. This can help in solving equations and performing other mathematical operations.
To simplify "Sqrt(xy)/y", you can start by factoring out the square root of xy from the numerator. This results in Sqrt(xy) * Sqrt(1/y). Then, you can simplify further by multiplying the two square roots together and reducing the fraction to Sqrt(x/y).
Yes, the expression "Sqrt(xy)/y" can be simplified further if x and y have common factors. In this case, you can divide both the numerator and denominator by the greatest common factor to reduce the fraction even more.
The only restriction for simplifying "Sqrt(xy)/y" is that the value of y cannot be equal to 0, as division by 0 is undefined. Other than that, this expression can be simplified for any real values of x and y.
Simplifying "Sqrt(xy)/y" can be useful in various real-life applications, such as in physics, engineering, and finance. For example, when calculating the force of gravity between two objects, this expression can be used to simplify the equation. In finance, it can be used to simplify compound interest calculations. In general, simplification helps in making complex calculations more manageable and understandable.