Solve for x 9=x square root of 3

$9 = x \sqrt{3}$

Step 1

Rewrite the equation as $x \sqrt{3} = 9$ .

$x \sqrt{3} = 9$

Step 2

Divide each term in $x \sqrt{3} = 9$ by $\sqrt{3}$ and simplify.

Divide each term in $x \sqrt{3} = 9$ by $\sqrt{3}$ .

$\frac{x \sqrt{3}}{\sqrt{3}} = \frac{9}{\sqrt{3}}$

Simplify the left side.

Cancel the common factor of $\sqrt{3}$ .

Cancel the common factor.

$\frac{x \sqrt{3}}{\sqrt{3}} = \frac{9}{\sqrt{3}}$

Divide $x$ by $1$ .

$x = \frac{9}{\sqrt{3}}$

Simplify the right side.

Multiply $\frac{9}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$x = \frac{9}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Combine and simplify the denominator.

Multiply $\frac{9}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$x = \frac{9 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$x = \frac{9 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$x = \frac{9 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{9 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$x = \frac{9 \sqrt{3}}{{\sqrt{3}}^{2}}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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

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

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

$x = \frac{9 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

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

$x = \frac{9 \sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \frac{9 \sqrt{3}}{3^{\frac{2}{2}}}$

Rewrite the expression.

$x = \frac{9 \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$x = \frac{9 \sqrt{3}}{3}$

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 \sqrt{3}$ .

$x = \frac{3 (3 \sqrt{3})}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$x = \frac{3 (3 \sqrt{3})}{3 (1)}$

Cancel the common factor.

$x = \frac{3 (3 \sqrt{3})}{3 \cdot 1}$

Rewrite the expression.

$x = \frac{3 \sqrt{3}}{1}$

Divide $3 \sqrt{3}$ by $1$ .

$x = 3 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{3}$

Decimal Form:

$x = 5.19615242 \dots$

Solve for x 9=x square root of 3

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