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

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

Evaluate

$$2\sqrt{7}\approx 5.291502622$$

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}.

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

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

$$11+\frac{\sqrt{7}\left(14-\sqrt{7}\right)}{7}-\sqrt[3]{1000}$$

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

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

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

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

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

$$\frac{77+14\sqrt{7}-7}{7}-\sqrt[3]{1000}$$

Do the calculations in 77+14\sqrt{7}-7.

$$\frac{70+14\sqrt{7}}{7}-\sqrt[3]{1000}$$

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

$$\frac{70+14\sqrt{7}}{7}-10$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{7}{7}.

$$\frac{70+14\sqrt{7}}{7}-\frac{10\times 7}{7}$$

Since \frac{70+14\sqrt{7}}{7} and \frac{10\times 7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{70+14\sqrt{7}-10\times 7}{7}$$

Do the multiplications in 70+14\sqrt{7}-10\times 7.

$$\frac{70+14\sqrt{7}-70}{7}$$

Do the calculations in 70+14\sqrt{7}-70.

$$\frac{14\sqrt{7}}{7}$$

Divide 14\sqrt{7} by 7 to get 2\sqrt{7}.

$$2\sqrt{7}$$