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Evaluate 3 square root of 8*3 square root of 10

$3 \sqrt{8} \cdot 3 \sqrt{10}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$3 \sqrt{4 (2)} \cdot (3 \sqrt{10})$

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

$3 \sqrt{2^{2} \cdot 2} \cdot (3 \sqrt{10})$

$3 \sqrt{2^{2} \cdot 2} \cdot (3 \sqrt{10})$

Step 2

Pull terms out from under the radical.

$3 (2 \sqrt{2}) \cdot (3 \sqrt{10})$

Step 3

Multiply $2$ by $3$ .

$6 \sqrt{2} \cdot (3 \sqrt{10})$

Step 4

Multiply $6 \sqrt{2} (3 \sqrt{10})$ .

Multiply $3$ by $6$ .

$18 \sqrt{2} \sqrt{10}$

Combine using the product rule for radicals.

$18 \sqrt{10 \cdot 2}$

Multiply $10$ by $2$ .

$18 \sqrt{20}$

$18 \sqrt{20}$

Step 5

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

Factor $4$ out of $20$ .

$18 \sqrt{4 (5)}$

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

$18 \sqrt{2^{2} \cdot 5}$

$18 \sqrt{2^{2} \cdot 5}$

Step 6

Pull terms out from under the radical.

$18 (2 \sqrt{5})$

Step 7

Multiply $2$ by $18$ .

$36 \sqrt{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$36 \sqrt{5}$

Decimal Form:

$80.49844718 \dots$

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