Given x > 0 express in simplest radical form with a rational denominator.
√336x^12/√7x^4
To express √336x^12/√7x^4 in simplest radical form with a rational denominator, we need to simplify the expression.
First, let's simplify the terms with square roots.
√336 can be written as √(16 * 21).
Since 16 is a perfect square, we can simplify it as 4.
So, √(16 * 21) becomes 4√21.
√7x^4 can be simplified by separating the terms.
Since x^4 is a perfect square, we can simplify it as x^2.
So, √7x^4 becomes √7 * x^2.
Now, let's simplify the entire expression.
We have 4√21x^12 divided by √7 * x^2.
Next, we can simplify the x terms by dividing x^12 by x^2.
So, x^12 divided by x^2 is x^(12-2) = x^10.
Now our expression becomes 4√21x^10 divided by √7.
Finally, to rationalize the denominator, we multiply the numerator and denominator by the conjugate of the denominator, which is √7.
This gives us (4√21x^10 * √7) / (√7 * √7).
Simplifying further, we have (4√21x^10√7) / 7.
Therefore, the expression in simplest radical form with a rational denominator is (4√21x^10√7) / 7.