Simplify 3 square root of 5c^3*(7 square root of 15c^2)

$3 \sqrt{5 c^{3}} \cdot (7 \sqrt{15 c^{2}})$

Step 1

Rewrite $5 c^{3}$ as $c^{2} \cdot (5 c)$ .

Factor out $c^{2}$ .

$3 \sqrt{5 (c^{2} c)} \cdot (7 \sqrt{15 c^{2}})$

Reorder $5$ and $c^{2}$ .

$3 \sqrt{c^{2} \cdot 5 c} \cdot (7 \sqrt{15 c^{2}})$

Add parentheses.

$3 \sqrt{c^{2} \cdot (5 c)} \cdot (7 \sqrt{15 c^{2}})$

Step 2

Pull terms out from under the radical.

$3 (c \sqrt{5 c}) \cdot (7 \sqrt{15 c^{2}})$

Step 3

Reorder $15$ and $c^{2}$ .

$3 c \sqrt{5 c} \cdot (7 \sqrt{c^{2} \cdot 15})$

Step 4

Pull terms out from under the radical.

$3 c \sqrt{5 c} \cdot (7 (c \sqrt{15}))$

Step 5

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$3 (c \cdot c) \sqrt{5 c} \cdot (7 (\sqrt{15}))$

Multiply $c$ by $c$ .

$3 c^{2} \sqrt{5 c} \cdot (7 (\sqrt{15}))$

Step 6

Multiply $3 c^{2} \sqrt{5 c} (7 \sqrt{15})$ .

Multiply $7$ by $3$ .

$21 c^{2} \sqrt{5 c} \sqrt{15}$

Combine using the product rule for radicals.

$21 c^{2} \sqrt{15 (5 c)}$

Multiply $15$ by $5$ .

$21 c^{2} \sqrt{75 c}$

Step 7

Rewrite $75 c$ as $5^{2} \cdot (3 c)$ .

Factor $25$ out of $75$ .

$21 c^{2} \sqrt{25 (3) c}$

Rewrite $25$ as $5^{2}$ .

$21 c^{2} \sqrt{5^{2} \cdot 3 c}$

Add parentheses.

$21 c^{2} \sqrt{5^{2} \cdot (3 c)}$

Step 8

Pull terms out from under the radical.

$21 c^{2} (5 \sqrt{3 c})$

Step 9

Multiply $5$ by $21$ .

$105 c^{2} \sqrt{3 c}$

Simplify 3 square root of 5c^3*(7 square root of 15c^2)

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