Solve (sqrt{0.06}divsqrt{6})*(sqrt{500}divsqrt{5})

$$( \sqrt{ 0.06 } \div \sqrt{ 6 } ) \times ( \sqrt{ 500 } \div \sqrt{ 5 } )$$

Evaluate

$$1$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{0.06}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\sqrt{0.06}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}\times \frac{\sqrt{500}}{\sqrt{5}}$$

The square of \sqrt{6} is 6.

$$\frac{\sqrt{0.06}\sqrt{6}}{6}\times \frac{\sqrt{500}}{\sqrt{5}}$$

To multiply \sqrt{0.06} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{0.36}}{6}\times \frac{\sqrt{500}}{\sqrt{5}}$$

Calculate the square root of 0.36 and get 0.6.

$$\frac{0.6}{6}\times \frac{\sqrt{500}}{\sqrt{5}}$$

Expand \frac{0.6}{6} by multiplying both numerator and the denominator by 10.

$$\frac{6}{60}\times \frac{\sqrt{500}}{\sqrt{5}}$$

Reduce the fraction \frac{6}{60} to lowest terms by extracting and canceling out 6.

$$\frac{1}{10}\times \frac{\sqrt{500}}{\sqrt{5}}$$

Rewrite the division of square roots \frac{\sqrt{500}}{\sqrt{5}} as the square root of the division \sqrt{\frac{500}{5}} and perform the division.

$$\frac{1}{10}\sqrt{100}$$

Calculate the square root of 100 and get 10.

$$\frac{1}{10}\times 10$$

Cancel out 10 and 10.

$$1$$

Factor

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