Solve the Rational Equation for m 2+ square root of m-2=7

$2 + \sqrt{m - 2} = 7$

Move all terms not containing $\sqrt{m - 2}$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$\sqrt{m - 2} = 7 - 2$

Subtract $2$ from $7$ .

$\sqrt{m - 2} = 5$

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

${\sqrt{m - 2}}^{2} = 5^{2}$

Simplify each side of the equation.

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

${({(m - 2)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

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

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

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

${(m - 2)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(m - 2)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(m - 2)}^{1} = 5^{2}$

Simplify.

$m - 2 = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$m - 2 = 25$

Move all terms not containing $m$ to the right side of the equation.

Add $2$ to both sides of the equation.

$m = 25 + 2$

Add $25$ and $2$ .

$m = 27$