Solve the Rational Equation for h square root of 2h+7=5

$\sqrt{2 h + 7} = 5$

Step 1

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

${\sqrt{2 h + 7}}^{2} = 5^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 h + 7}$ as ${(2 h + 7)}^{\frac{1}{2}}$ .

${({(2 h + 7)}^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

Simplify ${({(2 h + 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 h + 7)}^{\frac{1}{2}})}^{2}$ .

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

${(2 h + 7)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 h + 7)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

${(2 h + 7)}^{1} = 5^{2}$

Simplify.

$2 h + 7 = 5^{2}$

Simplify the right side.

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

$2 h + 7 = 25$

Step 3

Solve for $h$ .

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

Subtract $7$ from both sides of the equation.

$2 h = 25 - 7$

Subtract $7$ from $25$ .

$2 h = 18$

Divide each term in $2 h = 18$ by $2$ and simplify.

Divide each term in $2 h = 18$ by $2$ .

$\frac{2 h}{2} = \frac{18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 h}{2} = \frac{18}{2}$

Divide $h$ by $1$ .

$h = \frac{18}{2}$

Simplify the right side.

Divide $18$ by $2$ .

$h = 9$