Solve for b T = square root of gb-6

$T = \sqrt{g b - 6}$

Step 1

Rewrite the equation as $\sqrt{g b - 6} = T$ .

$\sqrt{g b - 6} = T$

Step 2

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

${\sqrt{g b - 6}}^{2} = T^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{g b - 6}$ as ${(g b - 6)}^{\frac{1}{2}}$ .

${({(g b - 6)}^{\frac{1}{2}})}^{2} = T^{2}$

Simplify the left side.

Simplify ${({(g b - 6)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(g b - 6)}^{\frac{1}{2}})}^{2}$ .

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

${(g b - 6)}^{\frac{1}{2} \cdot 2} = T^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(g b - 6)}^{\frac{1}{2} \cdot 2} = T^{2}$

Rewrite the expression.

${(g b - 6)}^{1} = T^{2}$

Simplify.

$g b - 6 = T^{2}$

Step 4

Solve for $b$ .

Add $6$ to both sides of the equation.

$g b = T^{2} + 6$

Divide each term in $g b = T^{2} + 6$ by $g$ and simplify.

Divide each term in $g b = T^{2} + 6$ by $g$ .

$\frac{g b}{g} = \frac{T^{2}}{g} + \frac{6}{g}$

Simplify the left side.

Cancel the common factor of $g$ .

Cancel the common factor.

$\frac{g b}{g} = \frac{T^{2}}{g} + \frac{6}{g}$

Divide $b$ by $1$ .

$b = \frac{T^{2}}{g} + \frac{6}{g}$