Solve for b b = square root of 2b^2-64

$b = \sqrt{2 b^{2} - 64}$

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\sqrt{2 b^{2} - 64} = b$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 b^{2} - 64}}^{2} = b^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 b^{2} - 64}$ as ${(2 b^{2} - 64)}^{\frac{1}{2}}$ .

${({(2 b^{2} - 64)}^{\frac{1}{2}})}^{2} = b^{2}$

Simplify the left side.

Simplify ${({(2 b^{2} - 64)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 b^{2} - 64)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(2 b^{2} - 64)}^{\frac{1}{2} \cdot 2} = b^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 b^{2} - 64)}^{\frac{1}{2} \cdot 2} = b^{2}$

Rewrite the expression.

${(2 b^{2} - 64)}^{1} = b^{2}$

Simplify.

$2 b^{2} - 64 = b^{2}$

Solve for $b$ .

Move all terms containing $b$ to the left side of the equation.

Subtract $b^{2}$ from both sides of the equation.

$2 b^{2} - 64 - b^{2} = 0$

Subtract $b^{2}$ from $2 b^{2}$ .

$b^{2} - 64 = 0$

Add $64$ to both sides of the equation.

$b^{2} = 64$

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

$b = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$b = \pm \sqrt{8^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$b = \pm 8$

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.

$b = 8$

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

$b = - 8$

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

$b = 8, - 8$

Exclude the solutions that do not make $b = \sqrt{2 b^{2} - 64}$ true.

$b = 8$