Solve for b -7+ square root of 25b=3

$- 7 + \sqrt{25 b} = 3$

Step 1

Move all terms not containing $\sqrt{25 b}$ to the right side of the equation.

Add $7$ to both sides of the equation.

$\sqrt{25 b} = 3 + 7$

Add $3$ and $7$ .

$\sqrt{25 b} = 10$

Step 2

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

${\sqrt{25 b}}^{2} = 10^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{25 b}$ as ${(25 b)}^{\frac{1}{2}}$ .

${({(25 b)}^{\frac{1}{2}})}^{2} = 10^{2}$

Simplify the left side.

Simplify ${({(25 b)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(25 b)}^{\frac{1}{2}})}^{2}$ .

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

${(25 b)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(25 b)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

${(25 b)}^{1} = 10^{2}$

Simplify.

$25 b = 10^{2}$

Simplify the right side.

Raise $10$ to the power of $2$ .

$25 b = 100$

Step 4

Divide each term in $25 b = 100$ by $25$ and simplify.

Divide each term in $25 b = 100$ by $25$ .

$\frac{25 b}{25} = \frac{100}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 b}{25} = \frac{100}{25}$

Divide $b$ by $1$ .

$b = \frac{100}{25}$

Simplify the right side.

Divide $100$ by $25$ .

$b = 4$