Solve sqrt{15/70}*sqrt{28/60}

$$\sqrt { \frac { 15 } { 70 } } \times \sqrt { \frac { 28 } { 60 } }$$

Evaluate

$$\frac{\sqrt{10}}{10}\approx 0.316227766$$

Solution Steps

Reduce the fraction \frac{15}{70} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{3}{14}}\sqrt{\frac{28}{60}}$$

Rewrite the square root of the division \sqrt{\frac{3}{14}} as the division of square roots \frac{\sqrt{3}}{\sqrt{14}}.

$$\frac{\sqrt{3}}{\sqrt{14}}\sqrt{\frac{28}{60}}$$

Rationalize the denominator of \frac{\sqrt{3}}{\sqrt{14}} by multiplying numerator and denominator by \sqrt{14}.

$$\frac{\sqrt{3}\sqrt{14}}{\left(\sqrt{14}\right)^{2}}\sqrt{\frac{28}{60}}$$

The square of \sqrt{14} is 14.

$$\frac{\sqrt{3}\sqrt{14}}{14}\sqrt{\frac{28}{60}}$$

To multiply \sqrt{3} and \sqrt{14}, multiply the numbers under the square root.

$$\frac{\sqrt{42}}{14}\sqrt{\frac{28}{60}}$$

Reduce the fraction \frac{28}{60} to lowest terms by extracting and canceling out 4.

$$\frac{\sqrt{42}}{14}\sqrt{\frac{7}{15}}$$

Rewrite the square root of the division \sqrt{\frac{7}{15}} as the division of square roots \frac{\sqrt{7}}{\sqrt{15}}.

$$\frac{\sqrt{42}}{14}\times \frac{\sqrt{7}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\sqrt{42}}{14}\times \frac{\sqrt{7}\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\sqrt{42}}{14}\times \frac{\sqrt{7}\sqrt{15}}{15}$$

To multiply \sqrt{7} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{42}}{14}\times \frac{\sqrt{105}}{15}$$

Multiply \frac{\sqrt{42}}{14} times \frac{\sqrt{105}}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{42}\sqrt{105}}{14\times 15}$$

To multiply \sqrt{42} and \sqrt{105}, multiply the numbers under the square root.

$$\frac{\sqrt{4410}}{14\times 15}$$

Multiply 14 and 15 to get 210.

$$\frac{\sqrt{4410}}{210}$$

Factor 4410=21^{2}\times 10. Rewrite the square root of the product \sqrt{21^{2}\times 10} as the product of square roots \sqrt{21^{2}}\sqrt{10}. Take the square root of 21^{2}.

$$\frac{21\sqrt{10}}{210}$$

Divide 21\sqrt{10} by 210 to get \frac{1}{10}\sqrt{10}.

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