Pre-Algebra Examples

$\sqrt{27} \cdot \sqrt{54}$

Step 1

Combine using the product rule for radicals.

$\sqrt{27 \cdot 54}$

Step 2

Multiply $27$ by $54$ .

$\sqrt{1458}$

Step 3

Rewrite $1458$ as $27^{2} \cdot 2$ .

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Step 3.1

Factor $729$ out of $1458$ .

$\sqrt{729 (2)}$

Step 3.2

Rewrite $729$ as $27^{2}$ .

$\sqrt{27^{2} \cdot 2}$

$\sqrt{27^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$27 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$27 \sqrt{2}$

Decimal Form:

$38.18376618 \dots$

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