Solve 2^3*5^2sqrt{1/125}

$$2 ^ { 3 } \cdot 5 ^ { 2 } \sqrt { \frac { 1 } { 125 } }$$

Evaluate

$$8\sqrt{5}\approx 17.88854382$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$8\times 5^{2}\sqrt{\frac{1}{125}}$$

Calculate 5 to the power of 2 and get 25.

$$8\times 25\sqrt{\frac{1}{125}}$$

Multiply 8 and 25 to get 200.

$$200\sqrt{\frac{1}{125}}$$

Rewrite the square root of the division \sqrt{\frac{1}{125}} as the division of square roots \frac{\sqrt{1}}{\sqrt{125}}.

$$200\times \frac{\sqrt{1}}{\sqrt{125}}$$

Calculate the square root of 1 and get 1.

$$200\times \frac{1}{\sqrt{125}}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$200\times \frac{1}{5\sqrt{5}}$$

Rationalize the denominator of \frac{1}{5\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$200\times \frac{\sqrt{5}}{5\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$200\times \frac{\sqrt{5}}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$200\times \frac{\sqrt{5}}{25}$$

Cancel out 25, the greatest common factor in 200 and 25.

$$8\sqrt{5}$$