Simplify square root of 3* square root of 21

$\sqrt{3} \cdot \sqrt{21}$

Step 1

Combine using the product rule for radicals.

$\sqrt{3 \cdot 21}$

Step 2

Multiply $3$ by $21$ .

$\sqrt{63}$

Step 3

Rewrite $63$ as $3^{2} \cdot 7$ .

Factor $9$ out of $63$ .

$\sqrt{9 (7)}$

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

$\sqrt{3^{2} \cdot 7}$

$\sqrt{3^{2} \cdot 7}$

Step 4

Pull terms out from under the radical.

$3 \sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{7}$

Decimal Form:

$7.93725393 \dots$

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