Solve 8sqrt{600}*sqrt{1/5}

$$8 \sqrt{ 600 } \times \sqrt{ \frac{ 1 }{ 5 } }$$

Evaluate

$$16\sqrt{30}\approx 87.635609201$$

Solution Steps

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$8\times 10\sqrt{6}\sqrt{\frac{1}{5}}$$

Multiply 8 and 10 to get 80.

$$80\sqrt{6}\sqrt{\frac{1}{5}}$$

Rewrite the square root of the division \sqrt{\frac{1}{5}} as the division of square roots \frac{\sqrt{1}}{\sqrt{5}}.

$$80\sqrt{6}\times \frac{\sqrt{1}}{\sqrt{5}}$$

Calculate the square root of 1 and get 1.

$$80\sqrt{6}\times \frac{1}{\sqrt{5}}$$

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

$$80\sqrt{6}\times \frac{\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$80\sqrt{6}\times \frac{\sqrt{5}}{5}$$

Cancel out 5, the greatest common factor in 80 and 5.

$$16\sqrt{5}\sqrt{6}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$16\sqrt{30}$$