Solve for r 2 square root of r = square root of 3r+9

$2 \sqrt{r} = \sqrt{3 r + 9}$

Step 1

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

${(2 \sqrt{r})}^{2} = {\sqrt{3 r + 9}}^{2}$

Step 2

Simplify each side of the equation.

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

${(2 r^{\frac{1}{2}})}^{2} = {\sqrt{3 r + 9}}^{2}$

Simplify the left side.

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

Apply the product rule to $2 r^{\frac{1}{2}}$ .

$2^{2} {(r^{\frac{1}{2}})}^{2} = {\sqrt{3 r + 9}}^{2}$

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

$4 {(r^{\frac{1}{2}})}^{2} = {\sqrt{3 r + 9}}^{2}$

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

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

$4 r^{\frac{1}{2} \cdot 2} = {\sqrt{3 r + 9}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 r^{\frac{1}{2} \cdot 2} = {\sqrt{3 r + 9}}^{2}$

Rewrite the expression.

$4 r^{1} = {\sqrt{3 r + 9}}^{2}$

Simplify.

$4 r = {\sqrt{3 r + 9}}^{2}$

Simplify the right side.

Simplify ${\sqrt{3 r + 9}}^{2}$ .

Factor $3$ out of $3 r + 9$ .

Factor $3$ out of $3 r$ .

$4 r = {\sqrt{3 (r) + 9}}^{2}$

Factor $3$ out of $9$ .

$4 r = {\sqrt{3 r + 3 \cdot 3}}^{2}$

Factor $3$ out of $3 r + 3 \cdot 3$ .

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

Rewrite ${\sqrt{3 (r + 3)}}^{2}$ as $3 (r + 3)$ .

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$4 r = {(3 (r + 3))}^{1}$

Simplify.

$4 r = 3 (r + 3)$

Apply the distributive property.

$4 r = 3 r + 3 \cdot 3$

Multiply $3$ by $3$ .

$4 r = 3 r + 9$

Step 3

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

Subtract $3 r$ from both sides of the equation.

$4 r - 3 r = 9$

Subtract $3 r$ from $4 r$ .

$r = 9$

Solve for r 2 square root of r = square root of 3r+9

Related Questions

Support LCMGCF.com by disabling your adblocker.