Solve 711+1.96*3.4/sqrt{46224}

$$711 + 1.96 \times \frac { 3.4 } { \sqrt { 46224 } }$$

Evaluate

$$\frac{833\sqrt{321}}{481500}+711\approx 711.030995684$$

Solution Steps

Factor 46224=12^{2}\times 321. Rewrite the square root of the product \sqrt{12^{2}\times 321} as the product of square roots \sqrt{12^{2}}\sqrt{321}. Take the square root of 12^{2}.

$$711+1.96\times \frac{3.4}{12\sqrt{321}}$$

Rationalize the denominator of \frac{3.4}{12\sqrt{321}} by multiplying numerator and denominator by \sqrt{321}.

$$711+1.96\times \frac{3.4\sqrt{321}}{12\left(\sqrt{321}\right)^{2}}$$

The square of \sqrt{321} is 321.

$$711+1.96\times \frac{3.4\sqrt{321}}{12\times 321}$$

Multiply 12 and 321 to get 3852.

$$711+1.96\times \frac{3.4\sqrt{321}}{3852}$$

Divide 3.4\sqrt{321} by 3852 to get \frac{17}{19260}\sqrt{321}.

$$711+1.96\times \frac{17}{19260}\sqrt{321}$$

Multiply 1.96 and \frac{17}{19260} to get \frac{833}{481500}.

$$711+\frac{833}{481500}\sqrt{321}$$