Finite Math Examples

$\sqrt{6 + 2 n} - 2 = 2$

Step 1

Factor $2$ out of $6 + 2 n$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $6$ .

$\sqrt{2 \cdot 3 + 2 n} - 2 = 2$

Step 1.2

Factor $2$ out of $2 \cdot 3 + 2 n$ .

$\sqrt{2 (3 + n)} - 2 = 2$

Step 2

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

Tap for more steps...

Step 2.1

Add $2$ to both sides of the equation.

$\sqrt{2 (3 + n)} = 2 + 2$

Step 2.2

Add $2$ and $2$ .

$\sqrt{2 (3 + n)} = 4$

Step 3

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

${\sqrt{2 (3 + n)}}^{2} = 4^{2}$

Step 4

Simplify each side of the equation.

Tap for more steps...

Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 (3 + n)}$ as ${(2 (3 + n))}^{\frac{1}{2}}$ .

${({(2 (3 + n))}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Simplify ${({(2 (3 + n))}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 4.2.1.1

Multiply the exponents in ${({(2 (3 + n))}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 4.2.1.1.1

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

${(2 (3 + n))}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.1.1.2.1

Cancel the common factor.

${(2 (3 + n))}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(2 (3 + n))}^{1} = 4^{2}$

Step 4.2.1.2

Apply the distributive property.

${(2 \cdot 3 + 2 n)}^{1} = 4^{2}$

Step 4.2.1.3

Multiply.

Tap for more steps...

Step 4.2.1.3.1

Multiply $2$ by $3$ .

${(6 + 2 n)}^{1} = 4^{2}$

Step 4.2.1.3.2

Simplify.

$6 + 2 n = 4^{2}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Raise $4$ to the power of $2$ .

$6 + 2 n = 16$

Step 5

Solve for $n$ .

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

Subtract $6$ from both sides of the equation.

$2 n = 16 - 6$

Step 5.1.2

Subtract $6$ from $16$ .

$2 n = 10$

Step 5.2

Divide each term in $2 n = 10$ by $2$ and simplify.

Tap for more steps...

Step 5.2.1

Divide each term in $2 n = 10$ by $2$ .

$\frac{2 n}{2} = \frac{10}{2}$

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.2.1.1

Cancel the common factor.

$\frac{2 n}{2} = \frac{10}{2}$

Step 5.2.2.1.2

Divide $n$ by $1$ .

$n = \frac{10}{2}$

Step 5.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.3.1

Divide $10$ by $2$ .

$n = 5$

Step 6