Solve y^2=9^2+4^2

$${ y }^{ 2 } = { 9 }^{ 2 } + { 4 }^{ 2 }$$

Solve for y

$$y=\sqrt{97}\approx 9.848857802$$

$$y=-\sqrt{97}\approx -9.848857802$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$y^{2}=81+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$y^{2}=81+16$$

Add 81 and 16 to get 97.

$$y^{2}=97$$

Take the square root of both sides of the equation.

$$y=\sqrt{97} y=-\sqrt{97}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$y^{2}=81+4^{2}$$

Calculate 4 to the power of 2 and get 16.

$$y^{2}=81+16$$

Add 81 and 16 to get 97.

$$y^{2}=97$$

Subtract 97 from both sides.

$$y^{2}-97=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -97 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-97\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-97\right)}}{2}$$

Multiply -4 times -97.

$$y=\frac{0±\sqrt{388}}{2}$$

Take the square root of 388.

$$y=\frac{0±2\sqrt{97}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{97}}{2} when ± is plus.

$$y=\sqrt{97}$$

Now solve the equation y=\frac{0±2\sqrt{97}}{2} when ± is minus.

$$y=-\sqrt{97}$$

The equation is now solved.

$$y=\sqrt{97} y=-\sqrt{97}$$