Solve 1,5/sqrt{160}

$$\frac { 1,5 } { \sqrt { 160 } }$$

Evaluate

$$\frac{3\sqrt{10}}{80}\approx 0.118585412$$

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}.

$$\frac{1,5}{4\sqrt{10}}$$

Rationalize the denominator of \frac{1,5}{4\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{1,5\sqrt{10}}{4\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$\frac{1,5\sqrt{10}}{4\times 10}$$

Multiply 4 and 10 to get 40.

$$\frac{1,5\sqrt{10}}{40}$$

Divide 1,5\sqrt{10} by 40 to get 0,0375\sqrt{10}.

$$0,0375\sqrt{10}$$