Solve for b 10 = square root of b/9+10

$10 = \sqrt{\frac{b}{9}} + 10$

Step 1

Rewrite the equation as $\sqrt{\frac{b}{9}} + 10 = 10$ .

$\sqrt{\frac{b}{9}} + 10 = 10$

Step 2

Move all terms not containing $\sqrt{\frac{b}{9}}$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$\sqrt{\frac{b}{9}} = 10 - 10$

Subtract $10$ from $10$ .

$\sqrt{\frac{b}{9}} = 0$

Step 3

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

${\sqrt{\frac{b}{9}}}^{2} = 0^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{\frac{b}{9}}$ as ${(\frac{b}{9})}^{\frac{1}{2}}$ .

${({(\frac{b}{9})}^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the left side.

Simplify ${({(\frac{b}{9})}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(\frac{b}{9})}^{\frac{1}{2}})}^{2}$ .

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

${(\frac{b}{9})}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(\frac{b}{9})}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

${(\frac{b}{9})}^{1} = 0^{2}$

Simplify.

$\frac{b}{9} = 0^{2}$

Simplify the right side.

Raising $0$ to any positive power yields $0$ .

$\frac{b}{9} = 0$

Step 5

Set the numerator equal to zero.

$b = 0$