Question

use the quotient rule to simplify. assume all variables represent non - negative.
\\(\sqrt{\frac{80x^{3}}{49y^{2}}}\\)
\\(\sqrt{\frac{80x^{3}}{49y^{2}}}=\square\\)
(simplify your answer. type an exact answer, using radicals as needed. use

Explanation:

Step1: Apply quotient rule for radicals

$\sqrt{\frac{80x^3}{49y^2}} = \frac{\sqrt{80x^3}}{\sqrt{49y^2}}$

Step2: Simplify denominator radical

$\sqrt{49y^2} = 7y$

Step3: Factor numerator radicand

$\sqrt{80x^3} = \sqrt{16x^2 \cdot 5x}$

Step4: Simplify numerator radical

$\sqrt{16x^2 \cdot 5x} = 4x\sqrt{5x}$

Step5: Combine simplified terms

$\frac{4x\sqrt{5x}}{7y}$

Answer:

$\frac{4x\sqrt{5x}}{7y}$