Solve b^2=24^2+26^2

$$b ^ { 2 } = 24 ^ { 2 } + 26 ^ { 2 }$$

Solve for b

$$b=2\sqrt{313}\approx 35.383612026$$

$$b=-2\sqrt{313}\approx -35.383612026$$

Steps by Finding Square Root

Calculate 24 to the power of 2 and get 576.

$$b^{2}=576+26^{2}$$

Calculate 26 to the power of 2 and get 676.

$$b^{2}=576+676$$

Add 576 and 676 to get 1252.

$$b^{2}=1252$$

Take the square root of both sides of the equation.

$$b=2\sqrt{313} b=-2\sqrt{313}$$

Steps Using the Quadratic Formula

Calculate 24 to the power of 2 and get 576.

$$b^{2}=576+26^{2}$$

Calculate 26 to the power of 2 and get 676.

$$b^{2}=576+676$$

Add 576 and 676 to get 1252.

$$b^{2}=1252$$

Subtract 1252 from both sides.

$$b^{2}-1252=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1252 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-1252\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-1252\right)}}{2}$$

Multiply -4 times -1252.

$$b=\frac{0±\sqrt{5008}}{2}$$

Take the square root of 5008.

$$b=\frac{0±4\sqrt{313}}{2}$$

Now solve the equation b=\frac{0±4\sqrt{313}}{2} when ± is plus.

$$b=2\sqrt{313}$$

Now solve the equation b=\frac{0±4\sqrt{313}}{2} when ± is minus.

$$b=-2\sqrt{313}$$

The equation is now solved.

$$b=2\sqrt{313} b=-2\sqrt{313}$$