Solve for b 4^2+b^2=8^2

$4^{2} + b^{2} = 8^{2}$

Step 1

Raise $4$ to the power of $2$ .

$16 + b^{2} = 8^{2}$

Step 2

Raise $8$ to the power of $2$ .

$16 + b^{2} = 64$

Step 3

Move all terms not containing $b$ to the right side of the equation.

Subtract $16$ from both sides of the equation.

$b^{2} = 64 - 16$

Subtract $16$ from $64$ .

$b^{2} = 48$

Step 4

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$b = \pm \sqrt{48}$

Step 5

Simplify $\pm \sqrt{48}$ .

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$b = \pm \sqrt{16 (3)}$

Rewrite $16$ as $4^{2}$ .

$b = \pm \sqrt{4^{2} \cdot 3}$

Pull terms out from under the radical.

$b = \pm 4 \sqrt{3}$

Step 6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$b = 4 \sqrt{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$b = - 4 \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$b = 4 \sqrt{3}, - 4 \sqrt{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$b = 4 \sqrt{3}, - 4 \sqrt{3}$

Decimal Form:

$b = 6.92820323 \dots, - 6.92820323 \dots$