Simplify 5 square root of 2*9 square root of 6

$5 \sqrt{2} \cdot 9 \sqrt{6}$

Step 1

Multiply $5 \sqrt{2} (9 \sqrt{6})$ .

Multiply $9$ by $5$ .

$45 \sqrt{2} \sqrt{6}$

Combine using the product rule for radicals.

$45 \sqrt{6 \cdot 2}$

Multiply $6$ by $2$ .

$45 \sqrt{12}$

$45 \sqrt{12}$

Step 2

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$45 \sqrt{4 (3)}$

Rewrite $4$ as $2^{2}$ .

$45 \sqrt{2^{2} \cdot 3}$

$45 \sqrt{2^{2} \cdot 3}$

Step 3

Pull terms out from under the radical.

$45 (2 \sqrt{3})$

Step 4

Multiply $2$ by $45$ .

$90 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$90 \sqrt{3}$

Decimal Form:

$155.88457268 \dots$

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