Solve p^2=11+2sqrt{3}0

$$p ^ { 2 } = 11 + 2 \sqrt { 3 } 0$$

Solve for p

$$p=\sqrt{11}\approx 3.31662479$$

$$p=-\sqrt{11}\approx -3.31662479$$

Steps by Finding Square Root

Multiply 0 and 2 to get 0.

$$p^{2}=11+0\sqrt{3}$$

Anything times zero gives zero.

$$p^{2}=11+0$$

Add 11 and 0 to get 11.

$$p^{2}=11$$

Take the square root of both sides of the equation.

$$p=\sqrt{11} p=-\sqrt{11}$$

Steps Using the Quadratic Formula

Multiply 0 and 2 to get 0.

$$p^{2}=11+0\sqrt{3}$$

Anything times zero gives zero.

$$p^{2}=11+0$$

Add 11 and 0 to get 11.

$$p^{2}=11$$

Subtract 11 from both sides.

$$p^{2}-11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-11\right)}}{2}$$

Square 0.

$$p=\frac{0±\sqrt{-4\left(-11\right)}}{2}$$

Multiply -4 times -11.

$$p=\frac{0±\sqrt{44}}{2}$$

Take the square root of 44.

$$p=\frac{0±2\sqrt{11}}{2}$$

Now solve the equation p=\frac{0±2\sqrt{11}}{2} when ± is plus.

$$p=\sqrt{11}$$

Now solve the equation p=\frac{0±2\sqrt{11}}{2} when ± is minus.

$$p=-\sqrt{11}$$

The equation is now solved.

$$p=\sqrt{11} p=-\sqrt{11}$$