Algebra Examples

$x \sqrt{3} = - 6 \sqrt{5}$

Step 1

Divide each term in $x \sqrt{3} = - 6 \sqrt{5}$ by $\sqrt{3}$ .

$\frac{x \sqrt{3}}{\sqrt{3}} = \frac{- 6 \sqrt{5}}{\sqrt{3}}$

Step 2

Simplify the left side.

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Step 2.1

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

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Step 2.1.1

Cancel the common factor.

$\frac{x \sqrt{3}}{\sqrt{3}} = \frac{- 6 \sqrt{5}}{\sqrt{3}}$

Step 2.1.2

Divide $x$ by $1$ .

$x = \frac{- 6 \sqrt{5}}{\sqrt{3}}$

Step 3

Simplify the right side.

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Step 3.1

Move the negative in front of the fraction.

$x = - \frac{6 \sqrt{5}}{\sqrt{3}}$

Step 3.2

Multiply $\frac{6 \sqrt{5}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$x = - (\frac{6 \sqrt{5}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 3.3

Combine and simplify the denominator.

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Step 3.3.1

Multiply $\frac{6 \sqrt{5}}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$x = - \frac{6 \sqrt{5} \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 3.3.2

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

$x = - \frac{6 \sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 3.3.3

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

$x = - \frac{6 \sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 3.3.4

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

$x = - \frac{6 \sqrt{5} \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 3.3.5

Add $1$ and $1$ .

$x = - \frac{6 \sqrt{5} \sqrt{3}}{{\sqrt{3}}^{2}}$

Step 3.3.6

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

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Step 3.3.6.1

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

$x = - \frac{6 \sqrt{5} \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 3.3.6.2

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

$x = - \frac{6 \sqrt{5} \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 3.3.6.3

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

$x = - \frac{6 \sqrt{5} \sqrt{3}}{3^{\frac{2}{2}}}$

Step 3.3.6.4

Cancel the common factor of $2$ .

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Step 3.3.6.4.1

Cancel the common factor.

$x = - \frac{6 \sqrt{5} \sqrt{3}}{3^{\frac{2}{2}}}$

Step 3.3.6.4.2

Rewrite the expression.

$x = - \frac{6 \sqrt{5} \sqrt{3}}{3^{1}}$

Step 3.3.6.5

Evaluate the exponent.

$x = - \frac{6 \sqrt{5} \sqrt{3}}{3}$

Step 3.4

Cancel the common factor of $6$ and $3$ .

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Step 3.4.1

Factor $3$ out of $6 \sqrt{5} \sqrt{3}$ .

$x = - \frac{3 (2 \sqrt{5} \sqrt{3})}{3}$

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor $3$ out of $3$ .

$x = - \frac{3 (2 \sqrt{5} \sqrt{3})}{3 (1)}$

Step 3.4.2.2

Cancel the common factor.

$x = - \frac{3 (2 \sqrt{5} \sqrt{3})}{3 \cdot 1}$

Step 3.4.2.3

Rewrite the expression.

$x = - \frac{2 \sqrt{5} \sqrt{3}}{1}$

Step 3.4.2.4

Divide $2 \sqrt{5} \sqrt{3}$ by $1$ .

$x = - (2 \sqrt{5} \sqrt{3})$

Step 3.5

Multiply $2 \sqrt{5} \sqrt{3}$ .

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Step 3.5.1

Combine using the product rule for radicals.

$x = - (2 \sqrt{3 \cdot 5})$

Step 3.5.2

Multiply $3$ by $5$ .

$x = - (2 \sqrt{15})$

Step 3.6

Multiply $2$ by $- 1$ .

$x = - 2 \sqrt{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 2 \sqrt{15}$

Decimal Form:

$x = - 7.74596669 \dots$