Solve sqrt{56/149}*12/3-(3/5)^2=

$$\sqrt { \frac { 56 } { 149 } } \cdot \frac { 12 } { 3 } - ( \frac { 3 } { 5 } ) ^ { 2 } =$$

Evaluate

$$\frac{8\sqrt{2086}}{149}-\frac{9}{25}\approx 2.092228134$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{56}{149}} as the division of square roots \frac{\sqrt{56}}{\sqrt{149}}.

$$\frac{\sqrt{56}}{\sqrt{149}}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

Factor 56=2^{2}\times 14. Rewrite the square root of the product \sqrt{2^{2}\times 14} as the product of square roots \sqrt{2^{2}}\sqrt{14}. Take the square root of 2^{2}.

$$\frac{2\sqrt{14}}{\sqrt{149}}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

Rationalize the denominator of \frac{2\sqrt{14}}{\sqrt{149}} by multiplying numerator and denominator by \sqrt{149}.

$$\frac{2\sqrt{14}\sqrt{149}}{\left(\sqrt{149}\right)^{2}}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

The square of \sqrt{149} is 149.

$$\frac{2\sqrt{14}\sqrt{149}}{149}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

To multiply \sqrt{14} and \sqrt{149}, multiply the numbers under the square root.

$$\frac{2\sqrt{2086}}{149}\times \frac{12}{3}-\left(\frac{3}{5}\right)^{2}$$

Divide 12 by 3 to get 4.

$$\frac{2\sqrt{2086}}{149}\times 4-\left(\frac{3}{5}\right)^{2}$$

Express \frac{2\sqrt{2086}}{149}\times 4 as a single fraction.

$$\frac{2\sqrt{2086}\times 4}{149}-\left(\frac{3}{5}\right)^{2}$$

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{2\sqrt{2086}\times 4}{149}-\frac{9}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 149 and 25 is 3725. Multiply \frac{2\sqrt{2086}\times 4}{149} times \frac{25}{25}. Multiply \frac{9}{25} times \frac{149}{149}.

$$\frac{25\times 2\sqrt{2086}\times 4}{3725}-\frac{9\times 149}{3725}$$

Since \frac{25\times 2\sqrt{2086}\times 4}{3725} and \frac{9\times 149}{3725} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25\times 2\sqrt{2086}\times 4-9\times 149}{3725}$$

Do the multiplications in 25\times 2\sqrt{2086}\times 4-9\times 149.

$$\frac{200\sqrt{2086}-1341}{3725}$$

Factor

$$\frac{200 \sqrt{2086} - 1341}{3725} = 2.092228133512856$$