Question

divide and simplify. assume that all variables are positive.
\\(\frac{\sqrt{315x^{8}y^{7}}}{\sqrt{7x^{7}y^{3}}}\\)
\\(\frac{\sqrt{315x^{8}y^{7}}}{\sqrt{7x^{7}y^{3}}}=\square\\)
(type an exact answer, using radicals as needed. simplify your

Explanation:

Step1: Combine radicals into one

$\frac{\sqrt{315x^8y^7}}{\sqrt{7x^7y^3}} = \sqrt{\frac{315x^8y^7}{7x^7y^3}}$

Step2: Simplify the fraction inside

$\sqrt{45x^{8-7}y^{7-3}} = \sqrt{45xy^4}$

Step3: Factor into perfect squares

$\sqrt{9y^4 \cdot 5x} = \sqrt{9y^4} \cdot \sqrt{5x}$

Step4: Simplify perfect square roots

$3y^2\sqrt{5x}$

Answer:

$3y^2\sqrt{5x}$