Solve 28^2+53^2=b^2

$$28 ^ { 2 } + 53 ^ { 2 } = b ^ { 2 }$$

Solve for b

$$b=\sqrt{3593}\approx 59.941638283$$

$$b=-\sqrt{3593}\approx -59.941638283$$

Steps by Finding Square Root

Calculate 28 to the power of 2 and get 784.

$$784+53^{2}=b^{2}$$

Calculate 53 to the power of 2 and get 2809.

$$784+2809=b^{2}$$

Add 784 and 2809 to get 3593.

$$3593=b^{2}$$

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

$$b^{2}=3593$$

Take the square root of both sides of the equation.

$$b=\sqrt{3593} b=-\sqrt{3593}$$

Steps Using the Quadratic Formula

Calculate 28 to the power of 2 and get 784.

$$784+53^{2}=b^{2}$$

Calculate 53 to the power of 2 and get 2809.

$$784+2809=b^{2}$$

Add 784 and 2809 to get 3593.

$$3593=b^{2}$$

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

$$b^{2}=3593$$

Subtract 3593 from both sides.

$$b^{2}-3593=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3593 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-3593\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-3593\right)}}{2}$$

Multiply -4 times -3593.

$$b=\frac{0±\sqrt{14372}}{2}$$

Take the square root of 14372.

$$b=\frac{0±2\sqrt{3593}}{2}$$

Now solve the equation b=\frac{0±2\sqrt{3593}}{2} when ± is plus.

$$b=\sqrt{3593}$$

Now solve the equation b=\frac{0±2\sqrt{3593}}{2} when ± is minus.

$$b=-\sqrt{3593}$$

The equation is now solved.

$$b=\sqrt{3593} b=-\sqrt{3593}$$