Solve c^2=15^2+42^2

$$c ^ { 2 } = 15 ^ { 2 } + 42 ^ { 2 }$$

Solve for c

$$c=3\sqrt{221}\approx 44.598206242$$

$$c=-3\sqrt{221}\approx -44.598206242$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$c^{2}=225+42^{2}$$

Calculate 42 to the power of 2 and get 1764.

$$c^{2}=225+1764$$

Add 225 and 1764 to get 1989.

$$c^{2}=1989$$

Take the square root of both sides of the equation.

$$c=3\sqrt{221} c=-3\sqrt{221}$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$c^{2}=225+42^{2}$$

Calculate 42 to the power of 2 and get 1764.

$$c^{2}=225+1764$$

Add 225 and 1764 to get 1989.

$$c^{2}=1989$$

Subtract 1989 from both sides.

$$c^{2}-1989=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1989 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1989\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-1989\right)}}{2}$$

Multiply -4 times -1989.

$$c=\frac{0±\sqrt{7956}}{2}$$

Take the square root of 7956.

$$c=\frac{0±6\sqrt{221}}{2}$$

Now solve the equation c=\frac{0±6\sqrt{221}}{2} when ± is plus.

$$c=3\sqrt{221}$$

Now solve the equation c=\frac{0±6\sqrt{221}}{2} when ± is minus.

$$c=-3\sqrt{221}$$

The equation is now solved.

$$c=3\sqrt{221} c=-3\sqrt{221}$$