Evaluate square root of 45* square root of 10

$\sqrt{45} \cdot \sqrt{10}$

Step 1

Combine using the product rule for radicals.

$\sqrt{45 \cdot 10}$

Step 2

Multiply $45$ by $10$ .

$\sqrt{450}$

Step 3

Rewrite $450$ as $15^{2} \cdot 2$ .

Factor $225$ out of $450$ .

$\sqrt{225 (2)}$

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2} \cdot 2}$

$\sqrt{15^{2} \cdot 2}$

Step 4

Pull terms out from under the radical.

$15 \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{2}$

Decimal Form:

$21.21320343 \dots$

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