Solve 8+1.645(0.25/sqrt{20})

$$8+1.645( \frac{ 0.25 }{ \sqrt{ 20 } } )$$

Evaluate

$$\frac{329\sqrt{5}}{8000}+8\approx 8.091958296$$

Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$8+1.645\times \frac{0.25}{2\sqrt{5}}$$

Rationalize the denominator of \frac{0.25}{2\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$8+1.645\times \frac{0.25\sqrt{5}}{2\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$8+1.645\times \frac{0.25\sqrt{5}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$8+1.645\times \frac{0.25\sqrt{5}}{10}$$

Divide 0.25\sqrt{5} by 10 to get 0.025\sqrt{5}.

$$8+1.645\times 0.025\sqrt{5}$$

Multiply 1.645 and 0.025 to get 0.041125.

$$8+0.041125\sqrt{5}$$