Solve for n 3+ square root of n=13

$3 + \sqrt{n} = 13$

Step 1

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

Subtract $3$ from both sides of the equation.

$\sqrt{n} = 13 - 3$

Subtract $3$ from $13$ .

$\sqrt{n} = 10$

Step 2

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

${\sqrt{n}}^{2} = 10^{2}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

$n^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$n^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

$n^{1} = 10^{2}$

Simplify.

$n = 10^{2}$

Simplify the right side.

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

$n = 100$