Solve the Rational Equation for x 3 square root of x+3=15

$3 \sqrt{x} + 3 = 15$

Step 1

Move all terms not containing $3 \sqrt{x}$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$3 \sqrt{x} = 15 - 3$

Subtract $3$ from $15$ .

$3 \sqrt{x} = 12$

Step 2

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

${(3 \sqrt{x})}^{2} = 12^{2}$

Step 3

Simplify each side of the equation.

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

${(3 x^{\frac{1}{2}})}^{2} = 12^{2}$

Simplify the left side.

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

Apply the product rule to $3 x^{\frac{1}{2}}$ .

$3^{2} {(x^{\frac{1}{2}})}^{2} = 12^{2}$

Raise $3$ to the power of $2$ .

$9 {(x^{\frac{1}{2}})}^{2} = 12^{2}$

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

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

$9 x^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 x^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

$9 x^{1} = 12^{2}$

Simplify.

$9 x = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$9 x = 144$

Step 4

Divide each term in $9 x = 144$ by $9$ and simplify.

Divide each term in $9 x = 144$ by $9$ .

$\frac{9 x}{9} = \frac{144}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{144}{9}$

Divide $x$ by $1$ .

$x = \frac{144}{9}$

Simplify the right side.

Divide $144$ by $9$ .

$x = 16$

Solve the Rational Equation for x 3 square root of x+3=15

Related Questions

Support LCMGCF.com by disabling your adblocker.