Solve {c}{sqrt{1/7}*sqrt{28}}{+sqrt{70}}

$$\left. \begin{array} { c } { \sqrt { \frac { 1 } { 7 } } \times \sqrt { 28 } } \\ { + \sqrt { 70 } } \end{array} \right.$$

Evaluate

$$\sqrt{70}+2\approx 10.366600265$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{7}} as the division of square roots \frac{\sqrt{1}}{\sqrt{7}}.

$$\frac{\sqrt{1}}{\sqrt{7}}\sqrt{28}+\sqrt{70}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{7}}\sqrt{28}+\sqrt{70}$$

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

$$\frac{\sqrt{7}}{\left(\sqrt{7}\right)^{2}}\sqrt{28}+\sqrt{70}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{7}}{7}\sqrt{28}+\sqrt{70}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{\sqrt{7}}{7}\times 2\sqrt{7}+\sqrt{70}$$

Express \frac{\sqrt{7}}{7}\times 2 as a single fraction.

$$\frac{\sqrt{7}\times 2}{7}\sqrt{7}+\sqrt{70}$$

Express \frac{\sqrt{7}\times 2}{7}\sqrt{7} as a single fraction.

$$\frac{\sqrt{7}\times 2\sqrt{7}}{7}+\sqrt{70}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{70} times \frac{7}{7}.

$$\frac{\sqrt{7}\times 2\sqrt{7}}{7}+\frac{7\sqrt{70}}{7}$$

Since \frac{\sqrt{7}\times 2\sqrt{7}}{7} and \frac{7\sqrt{70}}{7} have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{7}\times 2\sqrt{7}+7\sqrt{70}}{7}$$

Do the multiplications in \sqrt{7}\times 2\sqrt{7}+7\sqrt{70}.

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

Divide each term of 14+7\sqrt{70} by 7 to get 2+\sqrt{70}.

$$2+\sqrt{70}$$