Solve 12^2+4^2=f^2

$$12 ^ { 2 } + 4 ^ { 2 } = f ^ { 2 }$$

Solve for f

$$f=4\sqrt{10}\approx 12.649110641$$

$$f=-4\sqrt{10}\approx -12.649110641$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$144+4^{2}=f^{2}$$

Calculate 4 to the power of 2 and get 16.

$$144+16=f^{2}$$

Add 144 and 16 to get 160.

$$160=f^{2}$$

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

$$f^{2}=160$$

Take the square root of both sides of the equation.

$$f=4\sqrt{10} f=-4\sqrt{10}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$144+4^{2}=f^{2}$$

Calculate 4 to the power of 2 and get 16.

$$144+16=f^{2}$$

Add 144 and 16 to get 160.

$$160=f^{2}$$

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

$$f^{2}=160$$

Subtract 160 from both sides.

$$f^{2}-160=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -160 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$f=\frac{0±\sqrt{0^{2}-4\left(-160\right)}}{2}$$

Square 0.

$$f=\frac{0±\sqrt{-4\left(-160\right)}}{2}$$

Multiply -4 times -160.

$$f=\frac{0±\sqrt{640}}{2}$$

Take the square root of 640.

$$f=\frac{0±8\sqrt{10}}{2}$$

Now solve the equation f=\frac{0±8\sqrt{10}}{2} when ± is plus.

$$f=4\sqrt{10}$$

Now solve the equation f=\frac{0±8\sqrt{10}}{2} when ± is minus.

$$f=-4\sqrt{10}$$

The equation is now solved.

$$f=4\sqrt{10} f=-4\sqrt{10}$$