Solve 0.5sqrt{0.04+1/6}sqrt{144}

$$0.5 \sqrt{ 0.04+ \frac{ 1 }{ 6 } } \sqrt{ 144 }$$

Evaluate

$$\frac{\sqrt{186}}{5}\approx 2.727636339$$

Solution Steps

Convert decimal number 0.04 to fraction \frac{4}{100}. Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$0.5\sqrt{\frac{1}{25}+\frac{1}{6}}\sqrt{144}$$

Least common multiple of 25 and 6 is 150. Convert \frac{1}{25} and \frac{1}{6} to fractions with denominator 150.

$$0.5\sqrt{\frac{6}{150}+\frac{25}{150}}\sqrt{144}$$

Since \frac{6}{150} and \frac{25}{150} have the same denominator, add them by adding their numerators.

$$0.5\sqrt{\frac{6+25}{150}}\sqrt{144}$$

Add 6 and 25 to get 31.

$$0.5\sqrt{\frac{31}{150}}\sqrt{144}$$

Rewrite the square root of the division \sqrt{\frac{31}{150}} as the division of square roots \frac{\sqrt{31}}{\sqrt{150}}.

$$0.5\times \frac{\sqrt{31}}{\sqrt{150}}\sqrt{144}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$0.5\times \frac{\sqrt{31}}{5\sqrt{6}}\sqrt{144}$$

Rationalize the denominator of \frac{\sqrt{31}}{5\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$0.5\times \frac{\sqrt{31}\sqrt{6}}{5\left(\sqrt{6}\right)^{2}}\sqrt{144}$$

The square of \sqrt{6} is 6.

$$0.5\times \frac{\sqrt{31}\sqrt{6}}{5\times 6}\sqrt{144}$$

To multiply \sqrt{31} and \sqrt{6}, multiply the numbers under the square root.

$$0.5\times \frac{\sqrt{186}}{5\times 6}\sqrt{144}$$

Multiply 5 and 6 to get 30.

$$0.5\times \frac{\sqrt{186}}{30}\sqrt{144}$$

Calculate the square root of 144 and get 12.

$$0.5\times \frac{\sqrt{186}}{30}\times 12$$

Multiply 0.5 and 12 to get 6.

$$6\times \frac{\sqrt{186}}{30}$$

Cancel out 30, the greatest common factor in 6 and 30.

$$\frac{\sqrt{186}}{5}$$