Solve sqrt[10]{54*55*60*60*65*70*70*70*90*90}

$$\sqrt[ 10 ]{ 54 \cdot 55 \cdot 60 \cdot 60 \cdot 65 \cdot 70 \cdot 70 \cdot 70 \cdot 90 \cdot 90 }$$

Evaluate

$$2\sqrt[10]{1885608333984375}\approx 67.386848266$$

Solution Steps

Multiply 54 and 55 to get 2970.

$$\sqrt[10]{2970\times 60\times 60\times 65\times 70\times 70\times 70\times 90\times 90}$$

Multiply 2970 and 60 to get 178200.

$$\sqrt[10]{178200\times 60\times 65\times 70\times 70\times 70\times 90\times 90}$$

Multiply 178200 and 60 to get 10692000.

$$\sqrt[10]{10692000\times 65\times 70\times 70\times 70\times 90\times 90}$$

Multiply 10692000 and 65 to get 694980000.

$$\sqrt[10]{694980000\times 70\times 70\times 70\times 90\times 90}$$

Multiply 694980000 and 70 to get 48648600000.

$$\sqrt[10]{48648600000\times 70\times 70\times 90\times 90}$$

Multiply 48648600000 and 70 to get 3405402000000.

$$\sqrt[10]{3405402000000\times 70\times 90\times 90}$$

Multiply 3405402000000 and 70 to get 238378140000000.

$$\sqrt[10]{238378140000000\times 90\times 90}$$

Multiply 238378140000000 and 90 to get 21454032600000000.

$$\sqrt[10]{21454032600000000\times 90}$$

Multiply 21454032600000000 and 90 to get 1930862934000000000.

$$\sqrt[10]{1930862934000000000}$$