Solve 80/sqrt{40sqrt{170}}

$$\frac{ 80 }{ \sqrt{ 40 } \sqrt{ 170 } }$$

Evaluate

$$\frac{4\sqrt{17}}{17}\approx 0.9701425$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{80}{2\sqrt{10}\sqrt{170}}$$

Factor 170=10\times 17. Rewrite the square root of the product \sqrt{10\times 17} as the product of square roots \sqrt{10}\sqrt{17}.

$$\frac{80}{2\sqrt{10}\sqrt{10}\sqrt{17}}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$\frac{80}{2\times 10\sqrt{17}}$$

Rationalize the denominator of \frac{80}{2\times 10\sqrt{17}} by multiplying numerator and denominator by \sqrt{17}.

$$\frac{80\sqrt{17}}{2\times 10\left(\sqrt{17}\right)^{2}}$$

The square of \sqrt{17} is 17.

$$\frac{80\sqrt{17}}{2\times 10\times 17}$$

Cancel out 2\times 10 in both numerator and denominator.

$$\frac{4\sqrt{17}}{17}$$