Solve y^2=2^2+(sqrt{7})^2

$$y ^ { 2 } = 2 ^ { 2 } + ( \sqrt { 7 } ) ^ { 2 }$$

Solve for y

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

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

Steps by Finding Square Root

Calculate 2 to the power of 2 and get 4.

$$y^{2}=4+\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$y^{2}=4+7$$

Add 4 and 7 to get 11.

$$y^{2}=11$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate 2 to the power of 2 and get 4.

$$y^{2}=4+\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$y^{2}=4+7$$

Add 4 and 7 to get 11.

$$y^{2}=11$$

Subtract 11 from both sides.

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

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}.

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

Square 0.

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

Multiply -4 times -11.

$$y=\frac{0±\sqrt{44}}{2}$$

Take the square root of 44.

$$y=\frac{0±2\sqrt{11}}{2}$$

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

$$y=\sqrt{11}$$

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

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

The equation is now solved.

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