Solve frac{sqrt{300}}{1330/400}3/4+2/5=

$$\frac { \sqrt { 300 } } { \frac { 1330 } { 400 } } \frac { 3 } { 4 } + \frac { 2 } { 5 } =$$

Evaluate

$$\frac{300\sqrt{3}}{133}+\frac{2}{5}\approx 4.306881521$$

Short Solution Steps

Factor 300=10^{2}\times 3. Rewrite the square root of the product \sqrt{10^{2}\times 3} as the product of square roots \sqrt{10^{2}}\sqrt{3}. Take the square root of 10^{2}.

$$\frac{10\sqrt{3}}{\frac{1330}{400}}\times \frac{3}{4}+\frac{2}{5}$$

Reduce the fraction \frac{1330}{400} to lowest terms by extracting and canceling out 10.

$$\frac{10\sqrt{3}}{\frac{133}{40}}\times \frac{3}{4}+\frac{2}{5}$$

Divide 10\sqrt{3} by \frac{133}{40} by multiplying 10\sqrt{3} by the reciprocal of \frac{133}{40}.

$$\frac{10\sqrt{3}\times 40}{133}\times \frac{3}{4}+\frac{2}{5}$$

Multiply 10 and 40 to get 400.

$$\frac{400\sqrt{3}}{133}\times \frac{3}{4}+\frac{2}{5}$$

Multiply \frac{400\sqrt{3}}{133} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{400\sqrt{3}\times 3}{133\times 4}+\frac{2}{5}$$

Cancel out 4 in both numerator and denominator.

$$\frac{3\times 100\sqrt{3}}{133}+\frac{2}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 133 and 5 is 665. Multiply \frac{3\times 100\sqrt{3}}{133} times \frac{5}{5}. Multiply \frac{2}{5} times \frac{133}{133}.

$$\frac{5\times 3\times 100\sqrt{3}}{665}+\frac{2\times 133}{665}$$

Since \frac{5\times 3\times 100\sqrt{3}}{665} and \frac{2\times 133}{665} have the same denominator, add them by adding their numerators.

$$\frac{5\times 3\times 100\sqrt{3}+2\times 133}{665}$$

Do the multiplications in 5\times 3\times 100\sqrt{3}+2\times 133.

$$\frac{1500\sqrt{3}+266}{665}$$

Factor

$$\frac{2 {(750 \sqrt{3} + 133)}}{665} = 4.3068815208320546$$