Answer:
[tex]\dfrac{6x\sqrt{y}}{y^4}[/tex]
Step-by-step explanation:
You are expected to factor out all of the squares. The expression under the radical can be multiplied by (y/y) in order to make the denominator a square.*
[tex]\displaystyle\sqrt{\frac{36x^2}{y^7}}=\sqrt{\frac{6^2x^2y}{y^8}}=\sqrt{\left(\frac{6x}{y^4}\right)^2y}\\\\=\frac{6x\sqrt{y}}{y^4}[/tex]
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* This is the general approach you use to "rationalize the denominator" of radical expressions. You multiply under the radical by 1 in the form of a suitable fraction so that the root of the denominator contains no radicals. (For square roots, you want the denominator to be a perfect square; for cube roots, you want the denominator to be a perfect cube, and so on.)
