Solve 68x^2/5sqrt{8}

$$\frac{ 68 { x }^{ 2 } }{ 5 \sqrt{ 8 } }$$

Evaluate

$$\frac{17\sqrt{2}x^{2}}{5}$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{68x^{2}}{5\times 2\sqrt{2}}$$

Multiply 5 and 2 to get 10.

$$\frac{68x^{2}}{10\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{34x^{2}}{5\sqrt{2}}$$

Rationalize the denominator of \frac{34x^{2}}{5\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{34x^{2}\sqrt{2}}{5\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{34x^{2}\sqrt{2}}{5\times 2}$$

Multiply 5 and 2 to get 10.

$$\frac{34x^{2}\sqrt{2}}{10}$$

Divide 34x^{2}\sqrt{2} by 10 to get \frac{17}{5}x^{2}\sqrt{2}.

$$\frac{17}{5}x^{2}\sqrt{2}$$

Differentiate w.r.t. x

$$\frac{34\sqrt{2}x}{5}$$