Solve (4/5+2sqrt{499/5})+(2(4/5+frac{2sqrt{49}}{5})-3)

$$( \frac { 4 } { 5 } + 2 \sqrt { \frac { 499 } { 5 } } ) + ( 2 ( \frac { 4 } { 5 } + \frac { 2 \sqrt { 49 } } { 5 } ) - 3 )$$

Evaluate

$$\frac{2\sqrt{2495}}{5}+5\approx 24.97998999$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{499}{5}} as the division of square roots \frac{\sqrt{499}}{\sqrt{5}}.

$$\frac{4}{5}+2\times \frac{\sqrt{499}}{\sqrt{5}}+2\left(\frac{4}{5}+\frac{2\sqrt{49}}{5}\right)-3$$

Rationalize the denominator of \frac{\sqrt{499}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{4}{5}+2\times \frac{\sqrt{499}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}+2\left(\frac{4}{5}+\frac{2\sqrt{49}}{5}\right)-3$$

The square of \sqrt{5} is 5.

$$\frac{4}{5}+2\times \frac{\sqrt{499}\sqrt{5}}{5}+2\left(\frac{4}{5}+\frac{2\sqrt{49}}{5}\right)-3$$

To multiply \sqrt{499} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{4}{5}+2\times \frac{\sqrt{2495}}{5}+2\left(\frac{4}{5}+\frac{2\sqrt{49}}{5}\right)-3$$

Express 2\times \frac{\sqrt{2495}}{5} as a single fraction.

$$\frac{4}{5}+\frac{2\sqrt{2495}}{5}+2\left(\frac{4}{5}+\frac{2\sqrt{49}}{5}\right)-3$$

Calculate the square root of 49 and get 7.

$$\frac{4}{5}+\frac{2\sqrt{2495}}{5}+2\left(\frac{4}{5}+\frac{2\times 7}{5}\right)-3$$

Multiply 2 and 7 to get 14.

$$\frac{4}{5}+\frac{2\sqrt{2495}}{5}+2\left(\frac{4}{5}+\frac{14}{5}\right)-3$$

Since \frac{4}{5} and \frac{14}{5} have the same denominator, add them by adding their numerators.

$$\frac{4}{5}+\frac{2\sqrt{2495}}{5}+2\times \frac{4+14}{5}-3$$

Add 4 and 14 to get 18.

$$\frac{4}{5}+\frac{2\sqrt{2495}}{5}+2\times \frac{18}{5}-3$$

Express 2\times \frac{18}{5} as a single fraction.

$$\frac{4}{5}+\frac{2\sqrt{2495}}{5}+\frac{2\times 18}{5}-3$$

Multiply 2 and 18 to get 36.

$$\frac{4}{5}+\frac{2\sqrt{2495}}{5}+\frac{36}{5}-3$$

Since \frac{4}{5} and \frac{36}{5} have the same denominator, add them by adding their numerators.

$$\frac{4+36}{5}+\frac{2\sqrt{2495}}{5}-3$$

Add 4 and 36 to get 40.

$$\frac{40}{5}+\frac{2\sqrt{2495}}{5}-3$$

Divide 40 by 5 to get 8.

$$8+\frac{2\sqrt{2495}}{5}-3$$

Subtract 3 from 8 to get 5.

$$5+\frac{2\sqrt{2495}}{5}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{5}{5}.

$$\frac{5\times 5}{5}+\frac{2\sqrt{2495}}{5}$$

Since \frac{5\times 5}{5} and \frac{2\sqrt{2495}}{5} have the same denominator, add them by adding their numerators.

$$\frac{5\times 5+2\sqrt{2495}}{5}$$

Do the multiplications in 5\times 5+2\sqrt{2495}.

$$\frac{25+2\sqrt{2495}}{5}$$

Factor

$$\frac{2 \sqrt{2495} + 25}{5} = 24.97998998998748$$