Simplify 5 square root of 14z^2*4 square root of 21z^3

$5 \sqrt{14 z^{2}} \cdot 4 \sqrt{21 z^{3}}$

Step 1

Reorder $14$ and $z^{2}$ .

$5 \sqrt{z^{2} \cdot 14} \cdot (4 \sqrt{21 z^{3}})$

Step 2

Pull terms out from under the radical.

$5 (z \sqrt{14}) \cdot (4 \sqrt{21 z^{3}})$

Step 3

Rewrite $21 z^{3}$ as $z^{2} \cdot (21 z)$ .

Factor out $z^{2}$ .

$5 z \sqrt{14} \cdot (4 \sqrt{21 (z^{2} z)})$

Reorder $21$ and $z^{2}$ .

$5 z \sqrt{14} \cdot (4 \sqrt{z^{2} \cdot 21 z})$

Add parentheses.

$5 z \sqrt{14} \cdot (4 \sqrt{z^{2} \cdot (21 z)})$

Step 4

Pull terms out from under the radical.

$5 z \sqrt{14} \cdot (4 (z \sqrt{21 z}))$

Step 5

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

$5 (z \cdot z) \sqrt{14} \cdot (4 (\sqrt{21 z}))$

Multiply $z$ by $z$ .

$5 z^{2} \sqrt{14} \cdot (4 (\sqrt{21 z}))$

Step 6

Multiply $5 z^{2} \sqrt{14} (4 \sqrt{21 z})$ .

Multiply $4$ by $5$ .

$20 z^{2} \sqrt{14} \sqrt{21 z}$

Combine using the product rule for radicals.

$20 z^{2} \sqrt{21 z \cdot 14}$

Multiply $14$ by $21$ .

$20 z^{2} \sqrt{294 z}$

Step 7

Rewrite $294 z$ as $7^{2} \cdot (6 z)$ .

Factor $49$ out of $294$ .

$20 z^{2} \sqrt{49 (6) z}$

Rewrite $49$ as $7^{2}$ .

$20 z^{2} \sqrt{7^{2} \cdot 6 z}$

Add parentheses.

$20 z^{2} \sqrt{7^{2} \cdot (6 z)}$

Step 8

Pull terms out from under the radical.

$20 z^{2} (7 \sqrt{6 z})$

Step 9

Multiply $7$ by $20$ .

$140 z^{2} \sqrt{6 z}$

Simplify 5 square root of 14z^2*4 square root of 21z^3

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