Solve the Rational Equation for x 4 square root of x=6

$4 \sqrt{x} = 6$

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

${(4 \sqrt{x})}^{2} = 6^{2}$

Simplify each side of the equation.

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

${(4 x^{\frac{1}{2}})}^{2} = 6^{2}$

Simplify the left side.

Simplify ${(4 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $4 x^{\frac{1}{2}}$ .

$4^{2} {(x^{\frac{1}{2}})}^{2} = 6^{2}$

Raise $4$ to the power of $2$ .

$16 {(x^{\frac{1}{2}})}^{2} = 6^{2}$

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

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

$16 x^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 x^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

$16 x^{1} = 6^{2}$

Simplify.

$16 x = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$16 x = 36$

Divide each term in $16 x = 36$ by $16$ and simplify.

Divide each term in $16 x = 36$ by $16$ .

$\frac{16 x}{16} = \frac{36}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{36}{16}$

Divide $x$ by $1$ .

$x = \frac{36}{16}$

Simplify the right side.

Cancel the common factor of $36$ and $16$ .

Factor $4$ out of $36$ .

$x = \frac{4 (9)}{16}$

Cancel the common factors.

Factor $4$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.25$

Mixed Number Form:

$x = 2 \frac{1}{4}$

Solve the Rational Equation for x 4 square root of x=6

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