Solve -7-sqrt{frac{143/3}}{10}

$$\frac{ -7- \sqrt{ \frac{ 143 }{ 3 } } }{ 10 }$$

Evaluate

$$-\frac{\sqrt{429}}{30}-\frac{7}{10}\approx -1.390410506$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{143}{3}} as the division of square roots \frac{\sqrt{143}}{\sqrt{3}}.

$$\frac{-7-\frac{\sqrt{143}}{\sqrt{3}}}{10}$$

Rationalize the denominator of \frac{\sqrt{143}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{-7-\frac{\sqrt{143}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}{10}$$

The square of \sqrt{3} is 3.

$$\frac{-7-\frac{\sqrt{143}\sqrt{3}}{3}}{10}$$

To multiply \sqrt{143} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{-7-\frac{\sqrt{429}}{3}}{10}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -7 times \frac{3}{3}.

$$\frac{-\frac{7\times 3}{3}-\frac{\sqrt{429}}{3}}{10}$$

Since -\frac{7\times 3}{3} and \frac{\sqrt{429}}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{-7\times 3-\sqrt{429}}{3}}{10}$$

Do the multiplications in -7\times 3-\sqrt{429}.

$$\frac{\frac{-21-\sqrt{429}}{3}}{10}$$

Express \frac{\frac{-21-\sqrt{429}}{3}}{10} as a single fraction.

$$\frac{-21-\sqrt{429}}{3\times 10}$$

Multiply 3 and 10 to get 30.

$$\frac{-21-\sqrt{429}}{30}$$