Solve x^2divsqrt{5*6div47}

$${ x }^{ 2 } \div \sqrt{ 5 \times 6 \div 47 }$$

Evaluate

$$\frac{\sqrt{1410}x^{2}}{30}$$

Solution Steps

Multiply 5 and 6 to get 30.

$$\frac{x^{2}}{\sqrt{\frac{30}{47}}}$$

Rewrite the square root of the division \sqrt{\frac{30}{47}} as the division of square roots \frac{\sqrt{30}}{\sqrt{47}}.

$$\frac{x^{2}}{\frac{\sqrt{30}}{\sqrt{47}}}$$

Rationalize the denominator of \frac{\sqrt{30}}{\sqrt{47}} by multiplying numerator and denominator by \sqrt{47}.

$$\frac{x^{2}}{\frac{\sqrt{30}\sqrt{47}}{\left(\sqrt{47}\right)^{2}}}$$

The square of \sqrt{47} is 47.

$$\frac{x^{2}}{\frac{\sqrt{30}\sqrt{47}}{47}}$$

To multiply \sqrt{30} and \sqrt{47}, multiply the numbers under the square root.

$$\frac{x^{2}}{\frac{\sqrt{1410}}{47}}$$

Divide x^{2} by \frac{\sqrt{1410}}{47} by multiplying x^{2} by the reciprocal of \frac{\sqrt{1410}}{47}.

$$\frac{x^{2}\times 47}{\sqrt{1410}}$$

Rationalize the denominator of \frac{x^{2}\times 47}{\sqrt{1410}} by multiplying numerator and denominator by \sqrt{1410}.

$$\frac{x^{2}\times 47\sqrt{1410}}{\left(\sqrt{1410}\right)^{2}}$$

The square of \sqrt{1410} is 1410.

$$\frac{x^{2}\times 47\sqrt{1410}}{1410}$$

Divide x^{2}\times 47\sqrt{1410} by 1410 to get x^{2}\times \frac{1}{30}\sqrt{1410}.

$$x^{2}\times \frac{1}{30}\sqrt{1410}$$

Differentiate w.r.t. x

$$\frac{\sqrt{1410}x}{15}$$