Solve {l}{-6}{-frac{10+sqrt{76}}{-2}}

$$\left. \begin{array} { l } { - 6 } \\ { - \frac { 10 + \sqrt { 76 } } { - 2 } } \end{array} \right.$$

Evaluate

$$\sqrt{19}-1\approx 3.358898944$$

Solution Steps

Factor 76=2^{2}\times 19. Rewrite the square root of the product \sqrt{2^{2}\times 19} as the product of square roots \sqrt{2^{2}}\sqrt{19}. Take the square root of 2^{2}.

$$-6-\frac{10+2\sqrt{19}}{-2}$$

Divide each term of 10+2\sqrt{19} by -2 to get -5-\sqrt{19}.

$$-6-\left(-5-\sqrt{19}\right)$$

To find the opposite of -5-\sqrt{19}, find the opposite of each term.

$$-6-\left(-5\right)-\left(-\sqrt{19}\right)$$

The opposite of -5 is 5.

$$-6+5-\left(-\sqrt{19}\right)$$

The opposite of -\sqrt{19} is \sqrt{19}.

$$-6+5+\sqrt{19}$$

Add -6 and 5 to get -1.

$$-1+\sqrt{19}$$

Factor

$$\sqrt{19} - 1 = 3.358898944$$