Solve x=sqrt{(66*33^2)/3300*10^-4}

$$x = \sqrt { \frac { ( 66 \times 33 ^ { 2 } ) } { 3300 \times 10 ^ { - 4 } } }$$

Solve for x

$$x=330\sqrt{2}\approx 466.690475583$$

Steps for Solving Linear Equation

Cancel out 66 in both numerator and denominator.

$$x=\sqrt{\frac{33^{2}}{50\times 10^{-4}}}$$

Calculate 33 to the power of 2 and get 1089.

$$x=\sqrt{\frac{1089}{50\times 10^{-4}}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$x=\sqrt{\frac{1089}{50\times \frac{1}{10000}}}$$

Multiply 50 and \frac{1}{10000} to get \frac{1}{200}.

$$x=\sqrt{\frac{1089}{\frac{1}{200}}}$$

Divide 1089 by \frac{1}{200} by multiplying 1089 by the reciprocal of \frac{1}{200}.

$$x=\sqrt{1089\times 200}$$

Multiply 1089 and 200 to get 217800.

$$x=\sqrt{217800}$$

Factor 217800=330^{2}\times 2. Rewrite the square root of the product \sqrt{330^{2}\times 2} as the product of square roots \sqrt{330^{2}}\sqrt{2}. Take the square root of 330^{2}.

$$x=330\sqrt{2}$$

Assign x

$$x≔330\sqrt{2}$$