Solve sqrt{121}+sqrt{7}*(2-1/sqrt{7})sqrt[3]{1000}

$$\sqrt { 121 } + \sqrt { 7 } \times ( 2 - \frac { 1 } { \sqrt { 7 } } ) \sqrt[ 3 ] { 1000 }$$

Evaluate

$$20\sqrt{7}+1\approx 53.915026221$$

Short Solution Steps

Calculate the square root of 121 and get 11.

$$11+\sqrt{7}\left(2-\frac{1}{\sqrt{7}}\right)\sqrt[3]{1000}$$

Rationalize the denominator of \frac{1}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$11+\sqrt{7}\left(2-\frac{\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\right)\sqrt[3]{1000}$$

The square of \sqrt{7} is 7.

$$11+\sqrt{7}\left(2-\frac{\sqrt{7}}{7}\right)\sqrt[3]{1000}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{7}{7}.

$$11+\sqrt{7}\left(\frac{2\times 7}{7}-\frac{\sqrt{7}}{7}\right)\sqrt[3]{1000}$$

Since \frac{2\times 7}{7} and \frac{\sqrt{7}}{7} have the same denominator, subtract them by subtracting their numerators.

$$11+\sqrt{7}\times \frac{2\times 7-\sqrt{7}}{7}\sqrt[3]{1000}$$

Do the multiplications in 2\times 7-\sqrt{7}.

$$11+\sqrt{7}\times \frac{14-\sqrt{7}}{7}\sqrt[3]{1000}$$

Calculate \sqrt[3]{1000} and get 10.

$$11+\sqrt{7}\times \frac{14-\sqrt{7}}{7}\times 10$$

Express \sqrt{7}\times \frac{14-\sqrt{7}}{7} as a single fraction.

$$11+\frac{\sqrt{7}\left(14-\sqrt{7}\right)}{7}\times 10$$

Express \frac{\sqrt{7}\left(14-\sqrt{7}\right)}{7}\times 10 as a single fraction.

$$11+\frac{\sqrt{7}\left(14-\sqrt{7}\right)\times 10}{7}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 11 times \frac{7}{7}.

$$\frac{11\times 7}{7}+\frac{\sqrt{7}\left(14-\sqrt{7}\right)\times 10}{7}$$

Since \frac{11\times 7}{7} and \frac{\sqrt{7}\left(14-\sqrt{7}\right)\times 10}{7} have the same denominator, add them by adding their numerators.

$$\frac{11\times 7+\sqrt{7}\left(14-\sqrt{7}\right)\times 10}{7}$$

Do the multiplications in 11\times 7+\sqrt{7}\left(14-\sqrt{7}\right)\times 10.

$$\frac{77+140\sqrt{7}-70}{7}$$

Do the calculations in 77+140\sqrt{7}-70.

$$\frac{7+140\sqrt{7}}{7}$$

Divide each term of 7+140\sqrt{7} by 7 to get 1+20\sqrt{7}.

$$1+20\sqrt{7}$$