Solve b^2=800^2-100^2

$${ b }^{ 2 } = { 800 }^{ 2 } - { 100 }^{ 2 }$$

Solve for b

$$b=300\sqrt{7}\approx 793.725393319$$

$$b=-300\sqrt{7}\approx -793.725393319$$

Steps by Finding Square Root

Calculate 800 to the power of 2 and get 640000.

$$b^{2}=640000-100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$b^{2}=640000-10000$$

Subtract 10000 from 640000 to get 630000.

$$b^{2}=630000$$

Take the square root of both sides of the equation.

$$b=300\sqrt{7} b=-300\sqrt{7}$$

Steps Using the Quadratic Formula

Calculate 800 to the power of 2 and get 640000.

$$b^{2}=640000-100^{2}$$

Calculate 100 to the power of 2 and get 10000.

$$b^{2}=640000-10000$$

Subtract 10000 from 640000 to get 630000.

$$b^{2}=630000$$

Subtract 630000 from both sides.

$$b^{2}-630000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -630000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-630000\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-630000\right)}}{2}$$

Multiply -4 times -630000.

$$b=\frac{0±\sqrt{2520000}}{2}$$

Take the square root of 2520000.

$$b=\frac{0±600\sqrt{7}}{2}$$

Now solve the equation b=\frac{0±600\sqrt{7}}{2} when ± is plus.

$$b=300\sqrt{7}$$

Now solve the equation b=\frac{0±600\sqrt{7}}{2} when ± is minus.

$$b=-300\sqrt{7}$$

The equation is now solved.

$$b=300\sqrt{7} b=-300\sqrt{7}$$