Solve c^2=(25)^2+(32)^2

$$c ^ { 2 } = ( 25 ) ^ { 2 } + ( 32 ) ^ { 2 }$$

Solve for c

$$c=\sqrt{1649}\approx 40.607881008$$

$$c=-\sqrt{1649}\approx -40.607881008$$

Steps by Finding Square Root

Calculate 25 to the power of 2 and get 625.

$$c^{2}=625+32^{2}$$

Calculate 32 to the power of 2 and get 1024.

$$c^{2}=625+1024$$

Add 625 and 1024 to get 1649.

$$c^{2}=1649$$

Take the square root of both sides of the equation.

$$c=\sqrt{1649} c=-\sqrt{1649}$$

Steps Using the Quadratic Formula

Calculate 25 to the power of 2 and get 625.

$$c^{2}=625+32^{2}$$

Calculate 32 to the power of 2 and get 1024.

$$c^{2}=625+1024$$

Add 625 and 1024 to get 1649.

$$c^{2}=1649$$

Subtract 1649 from both sides.

$$c^{2}-1649=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1649 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1649\right)}}{2}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-1649\right)}}{2}$$

Multiply -4 times -1649.

$$c=\frac{0±\sqrt{6596}}{2}$$

Take the square root of 6596.

$$c=\frac{0±2\sqrt{1649}}{2}$$

Now solve the equation c=\frac{0±2\sqrt{1649}}{2} when ± is plus.

$$c=\sqrt{1649}$$

Now solve the equation c=\frac{0±2\sqrt{1649}}{2} when ± is minus.

$$c=-\sqrt{1649}$$

The equation is now solved.

$$c=\sqrt{1649} c=-\sqrt{1649}$$