Simplify square root of 83 square root of 40 square root of 3

$\sqrt{8} \cdot 3 \sqrt{40} \cdot \sqrt{3}$

Step 1

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

Factor $4$ out of $8$ .

$\sqrt{4 (2)} \cdot (3 \sqrt{40}) \cdot \sqrt{3}$

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

$\sqrt{2^{2} \cdot 2} \cdot (3 \sqrt{40}) \cdot \sqrt{3}$

Step 2

Pull terms out from under the radical.

$2 \sqrt{2} \cdot (3 \sqrt{40}) \cdot \sqrt{3}$

Step 3

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

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

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $2$ by $3$ .

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

Step 6

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

Multiply $6$ by $2$ .

$12 \sqrt{2} \sqrt{10} \cdot \sqrt{3}$

Combine using the product rule for radicals.

$12 \sqrt{10 \cdot 2} \cdot \sqrt{3}$

Multiply $10$ by $2$ .

$12 \sqrt{20} \cdot \sqrt{3}$

Step 7

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

Factor $4$ out of $20$ .

$12 \sqrt{4 (5)} \cdot \sqrt{3}$

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

$12 \sqrt{2^{2} \cdot 5} \cdot \sqrt{3}$

Step 8

Pull terms out from under the radical.

$12 (2 \sqrt{5}) \cdot \sqrt{3}$

Step 9

Multiply $2$ by $12$ .

$24 \sqrt{5} \cdot \sqrt{3}$

Step 10

Multiply $24 \sqrt{5} \sqrt{3}$ .

Combine using the product rule for radicals.

$24 \sqrt{3 \cdot 5}$

Multiply $3$ by $5$ .

$24 \sqrt{15}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$24 \sqrt{15}$

Decimal Form:

$92.95160030 \dots$

Simplify square root of 8*3 square root of 40* square root of 3

Related Questions

Support LCMGCF.com by disabling your adblocker.

Simplify square root of 83 square root of 40 square root of 3