Solve 4sqrt{6}x^2div2sqrt{7/3}

$$4 \sqrt { 6 } x ^ { 2 } \div 2 \sqrt { \frac { 7 } { 3 } }$$

Evaluate

$$2\sqrt{14}x^{2}$$

Solution Steps

Divide 4\sqrt{6}x^{2} by 2 to get 2\sqrt{6}x^{2}.

$$2\sqrt{6}x^{2}\sqrt{\frac{7}{3}}$$

Rewrite the square root of the division \sqrt{\frac{7}{3}} as the division of square roots \frac{\sqrt{7}}{\sqrt{3}}.

$$2\sqrt{6}x^{2}\times \frac{\sqrt{7}}{\sqrt{3}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\sqrt{6}x^{2}\times \frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$2\sqrt{6}x^{2}\times \frac{\sqrt{7}\sqrt{3}}{3}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$2\sqrt{6}x^{2}\times \frac{\sqrt{21}}{3}$$

Express 2\times \frac{\sqrt{21}}{3} as a single fraction.

$$\frac{2\sqrt{21}}{3}\sqrt{6}x^{2}$$

Express \frac{2\sqrt{21}}{3}\sqrt{6} as a single fraction.

$$\frac{2\sqrt{21}\sqrt{6}}{3}x^{2}$$

Express \frac{2\sqrt{21}\sqrt{6}}{3}x^{2} as a single fraction.

$$\frac{2\sqrt{21}\sqrt{6}x^{2}}{3}$$

Differentiate w.r.t. x

$$4\sqrt{14}x$$