Solve 1014/sqrt{200}+1/4(175)^3=

$$\frac { 1014 } { \sqrt { 200 } } + \frac { 1 } { 4 ( 175 ) ^ { 3 } } =$$

Evaluate

$$\frac{507\sqrt{2}}{10}+\frac{1}{21437500}\approx 71.700627659$$

Short Solution Steps

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$\frac{1014}{10\sqrt{2}}+\frac{1}{4\times 175^{3}}$$

Rationalize the denominator of \frac{1014}{10\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1014\sqrt{2}}{10\left(\sqrt{2}\right)^{2}}+\frac{1}{4\times 175^{3}}$$

The square of \sqrt{2} is 2.

$$\frac{1014\sqrt{2}}{10\times 2}+\frac{1}{4\times 175^{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{507\sqrt{2}}{2\times 5}+\frac{1}{4\times 175^{3}}$$

Multiply 2 and 5 to get 10.

$$\frac{507\sqrt{2}}{10}+\frac{1}{4\times 175^{3}}$$

Calculate 175 to the power of 3 and get 5359375.

$$\frac{507\sqrt{2}}{10}+\frac{1}{4\times 5359375}$$

Multiply 4 and 5359375 to get 21437500.

$$\frac{507\sqrt{2}}{10}+\frac{1}{21437500}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 21437500 is 21437500. Multiply \frac{507\sqrt{2}}{10} times \frac{2143750}{2143750}.

$$\frac{2143750\times 507\sqrt{2}}{21437500}+\frac{1}{21437500}$$

Since \frac{2143750\times 507\sqrt{2}}{21437500} and \frac{1}{21437500} have the same denominator, add them by adding their numerators.

$$\frac{2143750\times 507\sqrt{2}+1}{21437500}$$

Do the multiplications in 2143750\times 507\sqrt{2}+1.

$$\frac{1086881250\sqrt{2}+1}{21437500}$$

Factor

$$\frac{1086881250 \sqrt{2} + 1}{21437500} = 71.70062765896316$$