Solve sqrt{3+5/7}-6

$$\sqrt { \frac { 3 + 5 } { 7 } } - 6$$

Evaluate

$$\frac{2\sqrt{14}}{7}-6\approx -4.930955032$$

Short Solution Steps

Add 3 and 5 to get 8.

$$\sqrt{\frac{8}{7}}-6$$

Rewrite the square root of the division \sqrt{\frac{8}{7}} as the division of square roots \frac{\sqrt{8}}{\sqrt{7}}.

$$\frac{\sqrt{8}}{\sqrt{7}}-6$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\sqrt{2}}{\sqrt{7}}-6$$

Rationalize the denominator of \frac{2\sqrt{2}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{2\sqrt{2}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}-6$$

The square of \sqrt{7} is 7.

$$\frac{2\sqrt{2}\sqrt{7}}{7}-6$$

To multiply \sqrt{2} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{2\sqrt{14}}{7}-6$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6 times \frac{7}{7}.

$$\frac{2\sqrt{14}}{7}-\frac{6\times 7}{7}$$

Since \frac{2\sqrt{14}}{7} and \frac{6\times 7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\sqrt{14}-6\times 7}{7}$$

Do the multiplications in 2\sqrt{14}-6\times 7.

$$\frac{2\sqrt{14}-42}{7}$$