Solve 1^2+1^2=C^2

$$1 ^ { 2 } + 1 ^ { 2 } = C ^ { 2 }$$

Solve for C

$$C=\sqrt{2}\approx 1.414213562$$

$$C=-\sqrt{2}\approx -1.414213562$$

Steps by Finding Square Root

Calculate 1 to the power of 2 and get 1.

$$1+1^{2}=C^{2}$$

Calculate 1 to the power of 2 and get 1.

$$1+1=C^{2}$$

Add 1 and 1 to get 2.

$$2=C^{2}$$

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

$$C^{2}=2$$

Take the square root of both sides of the equation.

$$C=\sqrt{2} C=-\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 1 to the power of 2 and get 1.

$$1+1^{2}=C^{2}$$

Calculate 1 to the power of 2 and get 1.

$$1+1=C^{2}$$

Add 1 and 1 to get 2.

$$2=C^{2}$$

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

$$C^{2}=2$$

Subtract 2 from both sides.

$$C^{2}-2=0$$

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

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

Square 0.

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

Multiply -4 times -2.

$$C=\frac{0±\sqrt{8}}{2}$$

Take the square root of 8.

$$C=\frac{0±2\sqrt{2}}{2}$$

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

$$C=\sqrt{2}$$

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

$$C=-\sqrt{2}$$

The equation is now solved.

$$C=\sqrt{2} C=-\sqrt{2}$$