Solve 1.2/sqrt{150}

$$\frac { 1.2 } { \sqrt { 150 } }$$

Evaluate

$$\frac{\sqrt{6}}{25}\approx 0.09797959$$

Solution Steps

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$\frac{1.2}{5\sqrt{6}}$$

Rationalize the denominator of \frac{1.2}{5\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{1.2\sqrt{6}}{5\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{1.2\sqrt{6}}{5\times 6}$$

Multiply 5 and 6 to get 30.

$$\frac{1.2\sqrt{6}}{30}$$

Divide 1.2\sqrt{6} by 30 to get 0.04\sqrt{6}.

$$0.04\sqrt{6}$$