Solve for m -5 = square root of m-7

$- 5 = \sqrt{m} - 7$

Step 1

Rewrite the equation as $\sqrt{m} - 7 = - 5$ .

$\sqrt{m} - 7 = - 5$

Step 2

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

Add $7$ to both sides of the equation.

$\sqrt{m} = - 5 + 7$

Add $- 5$ and $7$ .

$\sqrt{m} = 2$

Step 3

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

${\sqrt{m}}^{2} = 2^{2}$

Step 4

Simplify each side of the equation.

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

${(m^{\frac{1}{2}})}^{2} = 2^{2}$

Simplify the left side.

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

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

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

$m^{\frac{1}{2} \cdot 2} = 2^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$m^{\frac{1}{2} \cdot 2} = 2^{2}$

Rewrite the expression.

$m^{1} = 2^{2}$

Simplify.

$m = 2^{2}$

Simplify the right side.

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

$m = 4$