Solve the Rational Equation for x 3 square root of x=2

$3 \sqrt{x} = 2$

Step 1

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

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

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$9 x = 2^{2}$

Simplify the right side.

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

$9 x = 4$

Step 3

Divide each term in $9 x = 4$ by $9$ and simplify.

Divide each term in $9 x = 4$ by $9$ .

$\frac{9 x}{9} = \frac{4}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{4}{9}$

Divide $x$ by $1$ .

$x = \frac{4}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{9}$

Decimal Form:

$x = 0.\overline{4}$