Solve =sqrt{5.99(15(16)/12)(1/5+1/5)}

$$= \sqrt { 5.99 ( \frac { 15 ( 16 ) } { 12 } ) ( \frac { 1 } { 5 } + \frac { 1 } { 5 } ) }$$

Evaluate

$$\frac{\sqrt{1198}}{5}\approx 6.92242732$$

Solution Steps

Multiply 15 and 16 to get 240.

$$\sqrt{5.99\times \frac{240}{12}\left(\frac{1}{5}+\frac{1}{5}\right)}$$

Divide 240 by 12 to get 20.

$$\sqrt{5.99\times 20\left(\frac{1}{5}+\frac{1}{5}\right)}$$

Multiply 5.99 and 20 to get 119.8.

$$\sqrt{119.8\left(\frac{1}{5}+\frac{1}{5}\right)}$$

Since \frac{1}{5} and \frac{1}{5} have the same denominator, add them by adding their numerators.

$$\sqrt{119.8\times \frac{1+1}{5}}$$

Add 1 and 1 to get 2.

$$\sqrt{119.8\times \frac{2}{5}}$$

Convert decimal number 119.8 to fraction \frac{1198}{10}. Reduce the fraction \frac{1198}{10} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{599}{5}\times \frac{2}{5}}$$

Multiply \frac{599}{5} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{599\times 2}{5\times 5}}$$

Do the multiplications in the fraction \frac{599\times 2}{5\times 5}.

$$\sqrt{\frac{1198}{25}}$$

Rewrite the square root of the division \sqrt{\frac{1198}{25}} as the division of square roots \frac{\sqrt{1198}}{\sqrt{25}}.

$$\frac{\sqrt{1198}}{\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{\sqrt{1198}}{5}$$