Solve for b square root of 8b=b

$\sqrt{8 b} = b$

Step 1

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

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

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 b}$ as ${(8 b)}^{\frac{1}{2}}$ .

${({(8 b)}^{\frac{1}{2}})}^{2} = b^{2}$

Simplify the left side.

Simplify ${({(8 b)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(8 b)}^{\frac{1}{2}})}^{2}$ .

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

${(8 b)}^{\frac{1}{2} \cdot 2} = b^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(8 b)}^{\frac{1}{2} \cdot 2} = b^{2}$

Rewrite the expression.

${(8 b)}^{1} = b^{2}$

Simplify.

$8 b = b^{2}$

Step 3

Solve for $b$ .

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

$8 b - b^{2} = 0$

Factor the left side of the equation.

Let $u = b$ . Substitute $u$ for all occurrences of $b$ .

$8 u - u^{2} = 0$

Factor $u$ out of $8 u - u^{2}$ .

Factor $u$ out of $8 u$ .

$u \cdot 8 - u^{2} = 0$

Factor $u$ out of $- u^{2}$ .

$u \cdot 8 + u (- u) = 0$

Factor $u$ out of $u \cdot 8 + u (- u)$ .

$u (8 - u) = 0$

Replace all occurrences of $u$ with $b$ .

$b (8 - b) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$b = 0$

$8 - b = 0$

Set $b$ equal to $0$ .

$b = 0$

Set $8 - b$ equal to $0$ and solve for $b$ .

Set $8 - b$ equal to $0$ .

$8 - b = 0$

Solve $8 - b = 0$ for $b$ .

Subtract $8$ from both sides of the equation.

$- b = - 8$

Divide each term in $- b = - 8$ by $- 1$ and simplify.

Divide each term in $- b = - 8$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 8}{- 1}$

Divide $b$ by $1$ .

$b = \frac{- 8}{- 1}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$b = 8$

The final solution is all the values that make $b (8 - b) = 0$ true.

$b = 0, 8$

Solve for b square root of 8b=b

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