Algebra Examples

$\sqrt{10} \cdot \sqrt{15}$

Step 1

Combine using the product rule for radicals.

$\sqrt{10 \cdot 15}$

Step 2

Multiply $10$ by $15$ .

$\sqrt{150}$

Step 3

Rewrite $150$ as $5^{2} \cdot 6$ .

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Step 3.1

Factor $25$ out of $150$ .

$\sqrt{25 (6)}$

Step 3.2

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

$\sqrt{5^{2} \cdot 6}$

$\sqrt{5^{2} \cdot 6}$

Step 4

Pull terms out from under the radical.

$5 \sqrt{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{6}$

Decimal Form:

$12.24744871 \dots$

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