Solve 4^2=1^2+y^2

$$4 ^ { 2 } = 1 ^ { 2 } + y ^ { 2 }$$

Solve for y

$$y=\sqrt{15}\approx 3.872983346$$

$$y=-\sqrt{15}\approx -3.872983346$$

Steps by Finding Square Root

Calculate 4 to the power of 2 and get 16.

$$16=1^{2}+y^{2}$$

Calculate 1 to the power of 2 and get 1.

$$16=1+y^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$1+y^{2}=16$$

Subtract 1 from both sides.

$$y^{2}=16-1$$

Subtract 1 from 16 to get 15.

$$y^{2}=15$$

Take the square root of both sides of the equation.

$$y=\sqrt{15} y=-\sqrt{15}$$

Steps Using the Quadratic Formula

Calculate 4 to the power of 2 and get 16.

$$16=1^{2}+y^{2}$$

Calculate 1 to the power of 2 and get 1.

$$16=1+y^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$1+y^{2}=16$$

Subtract 16 from both sides.

$$1+y^{2}-16=0$$

Subtract 16 from 1 to get -15.

$$-15+y^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$y^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-15\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$y=\frac{0±\sqrt{60}}{2}$$

Take the square root of 60.

$$y=\frac{0±2\sqrt{15}}{2}$$

Now solve the equation y=\frac{0±2\sqrt{15}}{2} when ± is plus.

$$y=\sqrt{15}$$

Now solve the equation y=\frac{0±2\sqrt{15}}{2} when ± is minus.

$$y=-\sqrt{15}$$

The equation is now solved.

$$y=\sqrt{15} y=-\sqrt{15}$$