Solve 15000*0.25/1000*sqrt{1^2*39+0.8^2*31/39+31}=

$$\frac { 15000 * 0.25 } { 1000 } * \sqrt { \frac { 1 ^ { 2 } * 39 + 0.8 ^ { 2 } * 31 } { 39 + 31 } } =$$

Evaluate

$$\frac{3\sqrt{102970}}{280}\approx 3.438100597$$

Solution Steps

Multiply 15000 and 0.25 to get 3750.

$$\frac{3750}{1000}\sqrt{\frac{1^{2}\times 39+0.8^{2}\times 31}{39+31}}$$

Reduce the fraction \frac{3750}{1000} to lowest terms by extracting and canceling out 250.

$$\frac{15}{4}\sqrt{\frac{1^{2}\times 39+0.8^{2}\times 31}{39+31}}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{15}{4}\sqrt{\frac{1\times 39+0.8^{2}\times 31}{39+31}}$$

Multiply 1 and 39 to get 39.

$$\frac{15}{4}\sqrt{\frac{39+0.8^{2}\times 31}{39+31}}$$

Calculate 0.8 to the power of 2 and get 0.64.

$$\frac{15}{4}\sqrt{\frac{39+0.64\times 31}{39+31}}$$

Multiply 0.64 and 31 to get 19.84.

$$\frac{15}{4}\sqrt{\frac{39+19.84}{39+31}}$$

Add 39 and 19.84 to get 58.84.

$$\frac{15}{4}\sqrt{\frac{58.84}{39+31}}$$

Add 39 and 31 to get 70.

$$\frac{15}{4}\sqrt{\frac{58.84}{70}}$$

Expand \frac{58.84}{70} by multiplying both numerator and the denominator by 100.

$$\frac{15}{4}\sqrt{\frac{5884}{7000}}$$

Reduce the fraction \frac{5884}{7000} to lowest terms by extracting and canceling out 4.

$$\frac{15}{4}\sqrt{\frac{1471}{1750}}$$

Rewrite the square root of the division \sqrt{\frac{1471}{1750}} as the division of square roots \frac{\sqrt{1471}}{\sqrt{1750}}.

$$\frac{15}{4}\times \frac{\sqrt{1471}}{\sqrt{1750}}$$

Factor 1750=5^{2}\times 70. Rewrite the square root of the product \sqrt{5^{2}\times 70} as the product of square roots \sqrt{5^{2}}\sqrt{70}. Take the square root of 5^{2}.

$$\frac{15}{4}\times \frac{\sqrt{1471}}{5\sqrt{70}}$$

Rationalize the denominator of \frac{\sqrt{1471}}{5\sqrt{70}} by multiplying numerator and denominator by \sqrt{70}.

$$\frac{15}{4}\times \frac{\sqrt{1471}\sqrt{70}}{5\left(\sqrt{70}\right)^{2}}$$

The square of \sqrt{70} is 70.

$$\frac{15}{4}\times \frac{\sqrt{1471}\sqrt{70}}{5\times 70}$$

To multiply \sqrt{1471} and \sqrt{70}, multiply the numbers under the square root.

$$\frac{15}{4}\times \frac{\sqrt{102970}}{5\times 70}$$

Multiply 5 and 70 to get 350.

$$\frac{15}{4}\times \frac{\sqrt{102970}}{350}$$

Multiply \frac{15}{4} times \frac{\sqrt{102970}}{350} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\sqrt{102970}}{4\times 350}$$

Cancel out 5 in both numerator and denominator.

$$\frac{3\sqrt{102970}}{4\times 70}$$

Multiply 4 and 70 to get 280.

$$\frac{3\sqrt{102970}}{280}$$