Solve x^256sqrt{29/sqrt{37}}

$${ x }^{ 2 } 56 \sqrt{ \frac{ 29 }{ \sqrt{ 37 } } }$$

Evaluate

$$\frac{56\sqrt{29}\times 37^{\frac{3}{4}}x^{2}}{37}$$

Solution Steps

Rationalize the denominator of \frac{29}{\sqrt{37}} by multiplying numerator and denominator by \sqrt{37}.

$$56x^{2}\sqrt{\frac{29\sqrt{37}}{\left(\sqrt{37}\right)^{2}}}$$

The square of \sqrt{37} is 37.

$$56x^{2}\sqrt{\frac{29\sqrt{37}}{37}}$$

Differentiate w.r.t. x

$$\frac{112\sqrt{29}\times 37^{\frac{3}{4}}x}{37}$$