Solve (1.5+0.045)^3/sqrt{48.4-7.4}+0.029^2

$$\frac { ( 1.5 + 0.045 ) ^ { 3 } } { \sqrt { 48.4 - 7.4 } } + 0.029 ^ { 2 }$$

Evaluate

$$\frac{29503629\sqrt{41}}{328000000}+0.000841\approx 0.576802591$$

Solution Steps

Add 1.5 and 0.045 to get 1.545.

$$\frac{1.545^{3}}{\sqrt{48.4-7.4}}+0.029^{2}$$

Calculate 1.545 to the power of 3 and get 3.687953625.

$$\frac{3.687953625}{\sqrt{48.4-7.4}}+0.029^{2}$$

Subtract 7.4 from 48.4 to get 41.

$$\frac{3.687953625}{\sqrt{41}}+0.029^{2}$$

Rationalize the denominator of \frac{3.687953625}{\sqrt{41}} by multiplying numerator and denominator by \sqrt{41}.

$$\frac{3.687953625\sqrt{41}}{\left(\sqrt{41}\right)^{2}}+0.029^{2}$$

The square of \sqrt{41} is 41.

$$\frac{3.687953625\sqrt{41}}{41}+0.029^{2}$$

Divide 3.687953625\sqrt{41} by 41 to get \frac{29503629}{328000000}\sqrt{41}.

$$\frac{29503629}{328000000}\sqrt{41}+0.029^{2}$$

Calculate 0.029 to the power of 2 and get 0.000841.

$$\frac{29503629}{328000000}\sqrt{41}+0.000841$$