Solve 1024/sqrt{150}+1/4(150)^3=

$$\frac { 1024 } { \sqrt { 150 } } + \frac { 1 } { 4 ( 150 ) ^ { 3 } } =$$

Evaluate

$$\frac{512\sqrt{6}}{15}+\frac{1}{13500000}\approx 83.609249961$$

Short 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}.

$$\frac{1024}{5\sqrt{6}}+\frac{1}{4\times 150^{3}}$$

Rationalize the denominator of \frac{1024}{5\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{1024\sqrt{6}}{5\left(\sqrt{6}\right)^{2}}+\frac{1}{4\times 150^{3}}$$

The square of \sqrt{6} is 6.

$$\frac{1024\sqrt{6}}{5\times 6}+\frac{1}{4\times 150^{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{512\sqrt{6}}{3\times 5}+\frac{1}{4\times 150^{3}}$$

Multiply 3 and 5 to get 15.

$$\frac{512\sqrt{6}}{15}+\frac{1}{4\times 150^{3}}$$

Calculate 150 to the power of 3 and get 3375000.

$$\frac{512\sqrt{6}}{15}+\frac{1}{4\times 3375000}$$

Multiply 4 and 3375000 to get 13500000.

$$\frac{512\sqrt{6}}{15}+\frac{1}{13500000}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 15 and 13500000 is 13500000. Multiply \frac{512\sqrt{6}}{15} times \frac{900000}{900000}.

$$\frac{900000\times 512\sqrt{6}}{13500000}+\frac{1}{13500000}$$

Since \frac{900000\times 512\sqrt{6}}{13500000} and \frac{1}{13500000} have the same denominator, add them by adding their numerators.

$$\frac{900000\times 512\sqrt{6}+1}{13500000}$$

Do the multiplications in 900000\times 512\sqrt{6}+1.

$$\frac{460800000\sqrt{6}+1}{13500000}$$

Factor

$$\frac{460800000 \sqrt{6} + 1}{13500000} = 83.6092499610732$$