Simplify cube root of 7* cube root of 20* cube root of 14* cube root of 98

$\sqrt[3]{7} \cdot \sqrt[3]{20} \cdot \sqrt[3]{14} \cdot \sqrt[3]{98}$

Step 1

Combine using the product rule for radicals.

$\sqrt[3]{7 \cdot 20} \cdot \sqrt[3]{14} \cdot \sqrt[3]{98}$

Step 2

Combine using the product rule for radicals.

$\sqrt[3]{7 \cdot 20 \cdot 14} \cdot \sqrt[3]{98}$

Step 3

Combine using the product rule for radicals.

$\sqrt[3]{7 \cdot 20 \cdot 14 \cdot 98}$

Step 4

Multiply.

Multiply $7$ by $20$ .

$\sqrt[3]{140 \cdot 14 \cdot 98}$

Multiply $140$ by $14$ .

$\sqrt[3]{1960 \cdot 98}$

Multiply $1960$ by $98$ .

$\sqrt[3]{192080}$

Step 5

Rewrite $192080$ as $14^{3} \cdot 70$ .

Factor $2744$ out of $192080$ .

$\sqrt[3]{2744 (70)}$

Rewrite $2744$ as $14^{3}$ .

$\sqrt[3]{14^{3} \cdot 70}$

Step 6

Pull terms out from under the radical.

$14 \sqrt[3]{70}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$14 \sqrt[3]{70}$

Decimal Form:

$57.69799419 \dots$