Solve 11sqrt{10*10*9*7*7*5*5*4*3*2*2}

$$11 \sqrt{ 10 \cdot 10 \cdot 9 \cdot 7 \cdot 7 \cdot 5 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 2 }$$

Evaluate

$$46200\sqrt{3}\approx 80020.747309682$$

Solution Steps

Multiply 10 and 10 to get 100.

$$11\sqrt{100\times 9\times 7\times 7\times 5\times 5\times 4\times 3\times 2\times 2}$$

Multiply 100 and 9 to get 900.

$$11\sqrt{900\times 7\times 7\times 5\times 5\times 4\times 3\times 2\times 2}$$

Multiply 900 and 7 to get 6300.

$$11\sqrt{6300\times 7\times 5\times 5\times 4\times 3\times 2\times 2}$$

Multiply 6300 and 7 to get 44100.

$$11\sqrt{44100\times 5\times 5\times 4\times 3\times 2\times 2}$$

Multiply 44100 and 5 to get 220500.

$$11\sqrt{220500\times 5\times 4\times 3\times 2\times 2}$$

Multiply 220500 and 5 to get 1102500.

$$11\sqrt{1102500\times 4\times 3\times 2\times 2}$$

Multiply 1102500 and 4 to get 4410000.

$$11\sqrt{4410000\times 3\times 2\times 2}$$

Multiply 4410000 and 3 to get 13230000.

$$11\sqrt{13230000\times 2\times 2}$$

Multiply 13230000 and 2 to get 26460000.

$$11\sqrt{26460000\times 2}$$

Multiply 26460000 and 2 to get 52920000.

$$11\sqrt{52920000}$$

Factor 52920000=4200^{2}\times 3. Rewrite the square root of the product \sqrt{4200^{2}\times 3} as the product of square roots \sqrt{4200^{2}}\sqrt{3}. Take the square root of 4200^{2}.

$$11\times 4200\sqrt{3}$$

Multiply 11 and 4200 to get 46200.

$$46200\sqrt{3}$$