Solve the Rational Equation for X 3 square root of X=5

$3 \sqrt{X} = 5$

Step 1

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

${(3 \sqrt{X})}^{2} = 5^{2}$

Step 2

Simplify each side of the equation.

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

${(3 X^{\frac{1}{2}})}^{2} = 5^{2}$

Simplify the left side.

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

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

$3^{2} {(X^{\frac{1}{2}})}^{2} = 5^{2}$

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

$9 {(X^{\frac{1}{2}})}^{2} = 5^{2}$

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

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

$9 X^{\frac{1}{2} \cdot 2} = 5^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 X^{\frac{1}{2} \cdot 2} = 5^{2}$

Rewrite the expression.

$9 X^{1} = 5^{2}$

Simplify.

$9 X = 5^{2}$

Simplify the right side.

Raise $5$ to the power of $2$ .

$9 X = 25$

Step 3

Divide each term in $9 X = 25$ by $9$ and simplify.

Divide each term in $9 X = 25$ by $9$ .

$\frac{9 X}{9} = \frac{25}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 X}{9} = \frac{25}{9}$

Divide $X$ by $1$ .

$X = \frac{25}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$X = \frac{25}{9}$

Decimal Form:

$X = 2.\overline{7}$

Mixed Number Form:

$X = 2 \frac{7}{9}$