what is the simplified form of the following expression? assume x > 0.\n\\(\\sqrt4{\\frac{3}{2x}}\\)\n\\(\\fr…

what is the simplified form of the following expression? assume x > 0.\n\\(\\sqrt4{\\frac{3}{2x}}\\)\n\\(\\frac{\\sqrt4{6x}}{2x}\\)\n\\(\\frac{\\sqrt4{24x^{3}}}{2x}\\)\n\\(\\frac{\\sqrt4{24x^{3}}}{16x^{4}}\\)\n\\(\\sqrt4{12x^{2}}\\)

what is the simplified form of the following expression? assume x > 0.\n\\(\\sqrt4{\\frac{3}{2x}}\\)\n\\(\\frac{\\sqrt4{6x}}{2x}\\)\n\\(\\frac{\\sqrt4{24x^{3}}}{2x}\\)\n\\(\\frac{\\sqrt4{24x^{3}}}{16x^{4}}\\)\n\\(\\sqrt4{12x^{2}}\\)

Answer

Explanation:

Step1: Rationalize the denominator

Multiply the numerator and denominator inside the fourth - root by $2^{3}x^{3}$ to get rid of the fraction inside the root. $\sqrt[4]{\frac{3}{2x}}=\sqrt[4]{\frac{3\times2^{3}x^{3}}{2x\times2^{3}x^{3}}}=\sqrt[4]{\frac{24x^{3}}{2^{4}x^{4}}}$.

Step2: Simplify the fourth - root

Using the property $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$, we have $\sqrt[4]{\frac{24x^{3}}{2^{4}x^{4}}}=\frac{\sqrt[4]{24x^{3}}}{2x}$.

Answer:

$\frac{\sqrt[4]{24x^{3}}}{2x}$