Solve sqrt{149/25}*sqrt{25/100}*sqrt{27/10}

$$\sqrt { \frac { 149 } { 25 } } \cdot \sqrt { \frac { 25 } { 100 } } \cdot \sqrt { \frac { 27 } { 10 } }$$

Evaluate

$$\frac{3\sqrt{4470}}{100}\approx 2.005741758$$

Solution Steps

To multiply \sqrt{\frac{149}{25}} and \sqrt{\frac{27}{10}}, multiply the numbers under the square root.

$$\sqrt{\frac{4023}{250}}\sqrt{\frac{25}{100}}$$

Rewrite the square root of the division \sqrt{\frac{4023}{250}} as the division of square roots \frac{\sqrt{4023}}{\sqrt{250}}.

$$\frac{\sqrt{4023}}{\sqrt{250}}\sqrt{\frac{25}{100}}$$

Factor 4023=3^{2}\times 447. Rewrite the square root of the product \sqrt{3^{2}\times 447} as the product of square roots \sqrt{3^{2}}\sqrt{447}. Take the square root of 3^{2}.

$$\frac{3\sqrt{447}}{\sqrt{250}}\sqrt{\frac{25}{100}}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$\frac{3\sqrt{447}}{5\sqrt{10}}\sqrt{\frac{25}{100}}$$

Rationalize the denominator of \frac{3\sqrt{447}}{5\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$\frac{3\sqrt{447}\sqrt{10}}{5\left(\sqrt{10}\right)^{2}}\sqrt{\frac{25}{100}}$$

The square of \sqrt{10} is 10.

$$\frac{3\sqrt{447}\sqrt{10}}{5\times 10}\sqrt{\frac{25}{100}}$$

To multiply \sqrt{447} and \sqrt{10}, multiply the numbers under the square root.

$$\frac{3\sqrt{4470}}{5\times 10}\sqrt{\frac{25}{100}}$$

Multiply 5 and 10 to get 50.

$$\frac{3\sqrt{4470}}{50}\sqrt{\frac{25}{100}}$$

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{3\sqrt{4470}}{50}\sqrt{\frac{1}{4}}$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3\sqrt{4470}}{50}\times \frac{1}{2}$$

Multiply \frac{3\sqrt{4470}}{50} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\sqrt{4470}}{50\times 2}$$

Multiply 50 and 2 to get 100.

$$\frac{3\sqrt{4470}}{100}$$