Solve frac{sqrt{160}}{4^2}

$$\frac { \sqrt { 160 } } { 4 ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{10}}{4}\approx 0.790569415$$

Solution Steps

Factor 160=4^{2}\times 10. Rewrite the square root of the product \sqrt{4^{2}\times 10} as the product of square roots \sqrt{4^{2}}\sqrt{10}. Take the square root of 4^{2}.

$$\frac{4\sqrt{10}}{4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{4\sqrt{10}}{16}$$

Divide 4\sqrt{10} by 16 to get \frac{1}{4}\sqrt{10}.

$$\frac{1}{4}\sqrt{10}$$