Algebra Examples

$6 \sqrt{15} \div 2 \sqrt{5}$

Step 1

Rewrite the division as a fraction.

$\frac{6 \sqrt{15}}{2} \sqrt{5}$

Step 2

Cancel the common factor of $6$ and $2$ .

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Step 2.1

Factor $2$ out of $6 \sqrt{15}$ .

$\frac{2 (3 \sqrt{15})}{2} \sqrt{5}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2$ .

$\frac{2 (3 \sqrt{15})}{2 (1)} \sqrt{5}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (3 \sqrt{15})}{2 \cdot 1} \sqrt{5}$

Step 2.2.3

Rewrite the expression.

$\frac{3 \sqrt{15}}{1} \sqrt{5}$

Step 2.2.4

Divide $3 \sqrt{15}$ by $1$ .

$3 \sqrt{15} \sqrt{5}$

$3 \sqrt{15} \sqrt{5}$

$3 \sqrt{15} \sqrt{5}$

Step 3

Multiply $3 \sqrt{15} \sqrt{5}$ .

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Step 3.1

Combine using the product rule for radicals.

$3 \sqrt{5 \cdot 15}$

Step 3.2

Multiply $5$ by $15$ .

$3 \sqrt{75}$

$3 \sqrt{75}$

Step 4

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 4.1

Factor $25$ out of $75$ .

$3 \sqrt{25 (3)}$

Step 4.2

Rewrite $25$ as $5^{2}$ .

$3 \sqrt{5^{2} \cdot 3}$

$3 \sqrt{5^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$3 (| 5 | \sqrt{3})$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$3 (5 \sqrt{3})$

Step 7

Multiply $5$ by $3$ .

$15 \sqrt{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{3}$

Decimal Form:

$25.98076211 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$