Algebra Examples

$7 \sqrt{3} \cdot 9 \sqrt{15}$

Step 1

Multiply $7 \sqrt{3} (9 \sqrt{15})$ .

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Step 1.1

Multiply $9$ by $7$ .

$63 \sqrt{3} \sqrt{15}$

Step 1.2

Combine using the product rule for radicals.

$63 \sqrt{15 \cdot 3}$

Step 1.3

Multiply $15$ by $3$ .

$63 \sqrt{45}$

$63 \sqrt{45}$

Step 2

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 2.1

Factor $9$ out of $45$ .

$63 \sqrt{9 (5)}$

Step 2.2

Rewrite $9$ as $3^{2}$ .

$63 \sqrt{3^{2} \cdot 5}$

$63 \sqrt{3^{2} \cdot 5}$

Step 3

Pull terms out from under the radical.

$63 (3 \sqrt{5})$

Step 4

Multiply $3$ by $63$ .

$189 \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$189 \sqrt{5}$

Decimal Form:

$422.61684774 \dots$

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