Question

$\sqrt{\frac{{9x}^2}{{36y}^4}}÷\frac{2y}{{9x}^2}$ equals

• A. $\frac{x^2}{{3y}^2}$
• B. $\frac{9x^3}{{4y}^3}$
• C. $\frac{x}{{4y}^2}$
• D. $\frac{x^3}{{18y}^3}$

Answer 1

The correct option is B $\frac{9x^3}{{4y}^3}$

$\sqrt{\frac{9x^2}{36y^4}}÷\frac{2y}{9x^2}$
Taking the square root of the first fraction
$=$ $\frac{3x}{6y^2}÷\frac{2y}{9x^2}$
Changing the divide by to multiply by the reciprocal,
$\frac{3x}{6y^2}\times \frac{9x^2}{2y}$
$=$ $\frac{3x\times 9x^2}{6y^2\times 2y}$
$=$ $\frac{9x^3}{4y^3}$