Rationalize the denominator of each expression. Assume that all variables are positive.
I understand how to divide them, but don't exactly know how to rationalize them.
�ã3xy^2/�ã5xy^3
Thanks in advance.
To rationalize the denominator of the expression `3xy^2 / 5xy^3`, we need to eliminate the square root in the denominator.
The general strategy for rationalizing the denominator is to multiply both the numerator and the denominator of the fraction by a suitable expression so that the denominator becomes a perfect square. In this case, we need to multiply by an expression with the square root of `y^3`.
To do this, we can multiply the numerator and the denominator by the square root of `y^3`:
`(3xy^2 / 5xy^3) * (√y^3 / √y^3)`
Multiplying the numerators and the denominators, we get:
`(3xy^2 * √y^3) / (5xy^3 * √y^3)`
To simplify further, we can multiply like terms:
`(3xy^2 * √y^3) / (5xy^3 * √y^3) = (3 * x * y^2 * y^3 * √y) / (5 * x * y^3 * y^3)`
Simplifying the expression, we have:
`(3xy^2 * √y^3) / (5xy^3 * √y^3) = (3xy^5 * √y) / (5xy^6)`
Now, the expression is in rationalized form with no square roots in the denominator.