Solve sqrt{0.009*0.036*0.016*0.08/0.002*0.0008*0.0002}

$$\sqrt { \frac { 0.009 \times 0.036 \times 0.016 \times 0.08 } { 0.002 \times 0.0008 \times 0.0002 } }$$

Evaluate

$$36$$

Solution Steps

Multiply 0.009 and 0.036 to get 0.000324.

$$\sqrt{\frac{0.000324\times 0.016\times 0.08}{0.002\times 0.0008\times 0.0002}}$$

Multiply 0.000324 and 0.016 to get 0.000005184.

$$\sqrt{\frac{0.000005184\times 0.08}{0.002\times 0.0008\times 0.0002}}$$

Multiply 0.000005184 and 0.08 to get 0.00000041472.

$$\sqrt{\frac{0.00000041472}{0.002\times 0.0008\times 0.0002}}$$

Multiply 0.002 and 0.0008 to get 0.0000016.

$$\sqrt{\frac{0.00000041472}{0.0000016\times 0.0002}}$$

Multiply 0.0000016 and 0.0002 to get 0.00000000032.

$$\sqrt{\frac{0.00000041472}{0.00000000032}}$$

Expand \frac{0.00000041472}{0.00000000032} by multiplying both numerator and the denominator by 100000000000.

$$\sqrt{\frac{41472}{32}}$$

Divide 41472 by 32 to get 1296.

$$\sqrt{1296}$$

Calculate the square root of 1296 and get 36.

$$36$$

Factor

$$2^{2}\times 3^{2}$$