Solve sqrt{(216)^1/3(25)^3/(1/25)^-2/2}

$$\sqrt { \frac { ( 216 ) ^ { 1 / 3 } ( 25 ) ^ { 3 } } { ( 1 / 25 ) ^ { - 2 / 2 } } }$$

Evaluate

$$25\sqrt{6}\approx 61.23724357$$

Solution Steps

Divide 2 by 2 to get 1.

$$\sqrt{\frac{216^{\frac{1}{3}}\times 25^{3}}{\left(\frac{1}{25}\right)^{-1}}}$$

Calculate 216 to the power of \frac{1}{3} and get 6.

$$\sqrt{\frac{6\times 25^{3}}{\left(\frac{1}{25}\right)^{-1}}}$$

Calculate 25 to the power of 3 and get 15625.

$$\sqrt{\frac{6\times 15625}{\left(\frac{1}{25}\right)^{-1}}}$$

Multiply 6 and 15625 to get 93750.

$$\sqrt{\frac{93750}{\left(\frac{1}{25}\right)^{-1}}}$$

Calculate \frac{1}{25} to the power of -1 and get 25.

$$\sqrt{\frac{93750}{25}}$$

Divide 93750 by 25 to get 3750.

$$\sqrt{3750}$$

Factor 3750=25^{2}\times 6. Rewrite the square root of the product \sqrt{25^{2}\times 6} as the product of square roots \sqrt{25^{2}}\sqrt{6}. Take the square root of 25^{2}.

$$25\sqrt{6}$$