Simplify square root of 27(3 square root of 20)

$\sqrt{27} (3 \sqrt{20})$

Rewrite $27$ as $3^{2} \cdot 3$ .

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Factor $9$ out of $27$ .

$\sqrt{9 (3)} (3 \sqrt{20})$

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

$\sqrt{3^{2} \cdot 3} (3 \sqrt{20})$

Pull terms out from under the radical.

$3 \sqrt{3} (3 \sqrt{20})$

Rewrite $20$ as $2^{2} \cdot 5$ .

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Factor $4$ out of $20$ .

$3 \sqrt{3} (3 \sqrt{4 (5)})$

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

$3 \sqrt{3} (3 \sqrt{2^{2} \cdot 5})$

Pull terms out from under the radical.

$3 \sqrt{3} (3 (2 \sqrt{5}))$

Multiply $2$ by $3$ .

$3 \sqrt{3} (6 \sqrt{5})$

Multiply $3 \sqrt{3} (6 \sqrt{5})$ .

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Multiply $6$ by $3$ .

$18 \sqrt{3} \sqrt{5}$

Combine using the product rule for radicals.

$18 \sqrt{5 \cdot 3}$

Multiply $5$ by $3$ .

$18 \sqrt{15}$

The result can be shown in multiple forms.

Exact Form:

$18 \sqrt{15}$

Decimal Form:

$69.71370023 \dots$

Simplify square root of 27(3 square root of 20)

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