Algebra Examples

$3 x \sqrt{5} = 21 \sqrt{30}$

Step 1

Divide each term in $3 x \sqrt{5} = 21 \sqrt{30}$ by $3 \sqrt{5}$ .

$\frac{3 x \sqrt{5}}{3 \sqrt{5}} = \frac{21 \sqrt{30}}{3 \sqrt{5}}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $3$ .

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Step 2.1.1

Cancel the common factor.

$\frac{3 x \sqrt{5}}{3 \sqrt{5}} = \frac{21 \sqrt{30}}{3 \sqrt{5}}$

Step 2.1.2

Rewrite the expression.

$\frac{x \sqrt{5}}{\sqrt{5}} = \frac{21 \sqrt{30}}{3 \sqrt{5}}$

Step 2.2

Cancel the common factor of $\sqrt{5}$ .

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Step 2.2.1

Cancel the common factor.

$\frac{x \sqrt{5}}{\sqrt{5}} = \frac{21 \sqrt{30}}{3 \sqrt{5}}$

Step 2.2.2

Divide $x$ by $1$ .

$x = \frac{21 \sqrt{30}}{3 \sqrt{5}}$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $21$ and $3$ .

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Step 3.1.1

Factor $3$ out of $21 \sqrt{30}$ .

$x = \frac{3 (7 \sqrt{30})}{3 \sqrt{5}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

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

$x = \frac{3 (7 \sqrt{30})}{3 (\sqrt{5})}$

Step 3.1.2.2

Cancel the common factor.

$x = \frac{3 (7 \sqrt{30})}{3 \sqrt{5}}$

Step 3.1.2.3

Rewrite the expression.

$x = \frac{7 \sqrt{30}}{\sqrt{5}}$

Step 3.2

Combine $\sqrt{30}$ and $\sqrt{5}$ into a single radical.

$x = 7 \sqrt{\frac{30}{5}}$

Step 3.3

Divide $30$ by $5$ .

$x = 7 \sqrt{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 7 \sqrt{6}$

Decimal Form:

$x = 17.14642819 \dots$