Basic Math Examples

$\sqrt{4 r - 6} = \sqrt{r + 9}$

Step 1

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

${\sqrt{4 r - 6}}^{2} = {\sqrt{r + 9}}^{2}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 r - 6}$ as ${(4 r - 6)}^{\frac{1}{2}}$ .

${({(4 r - 6)}^{\frac{1}{2}})}^{2} = {\sqrt{r + 9}}^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${({(4 r - 6)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

Multiply the exponents in ${({(4 r - 6)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1.1

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

${(4 r - 6)}^{\frac{1}{2} \cdot 2} = {\sqrt{r + 9}}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

${(4 r - 6)}^{\frac{1}{2} \cdot 2} = {\sqrt{r + 9}}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(4 r - 6)}^{1} = {\sqrt{r + 9}}^{2}$

Step 2.2.1.2

Simplify.

$4 r - 6 = {\sqrt{r + 9}}^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Rewrite ${\sqrt{r + 9}}^{2}$ as $r + 9$ .

Tap for more steps...

Step 2.3.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{r + 9}$ as ${(r + 9)}^{\frac{1}{2}}$ .

$4 r - 6 = {({(r + 9)}^{\frac{1}{2}})}^{2}$

Step 2.3.1.2

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

$4 r - 6 = {(r + 9)}^{\frac{1}{2} \cdot 2}$

Step 2.3.1.3

Combine $\frac{1}{2}$ and $2$ .

$4 r - 6 = {(r + 9)}^{\frac{2}{2}}$

Step 2.3.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.3.1.4.1

Cancel the common factor.

$4 r - 6 = {(r + 9)}^{\frac{2}{2}}$

Step 2.3.1.4.2

Rewrite the expression.

$4 r - 6 = {(r + 9)}^{1}$

Step 2.3.1.5

Simplify.

$4 r - 6 = r + 9$

Step 3

Solve for $r$ .

Tap for more steps...

Step 3.1

Move all terms containing $r$ to the left side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $r$ from both sides of the equation.

$4 r - 6 - r = 9$

Step 3.1.2

Subtract $r$ from $4 r$ .

$3 r - 6 = 9$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Add $6$ to both sides of the equation.

$3 r = 9 + 6$

Step 3.2.2

Add $9$ and $6$ .

$3 r = 15$

Step 3.3

Divide each term in $3 r = 15$ by $3$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $3 r = 15$ by $3$ .

$\frac{3 r}{3} = \frac{15}{3}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 r}{3} = \frac{15}{3}$

Step 3.3.2.1.2

Divide $r$ by $1$ .

$r = \frac{15}{3}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Divide $15$ by $3$ .

$r = 5$