Solve sqrt{21/4}+1/2sqrt{0.36}

$$\sqrt { 2 \frac { 1 } { 4 } } + \frac { 1 } { 2 } \sqrt { 0.36 }$$

Evaluate

$$1.8$$

Solution Steps

Multiply 2 and 4 to get 8.

$$\sqrt{\frac{8+1}{4}}+\frac{1}{2}\sqrt{0.36}$$

Add 8 and 1 to get 9.

$$\sqrt{\frac{9}{4}}+\frac{1}{2}\sqrt{0.36}$$

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{3}{2}+\frac{1}{2}\sqrt{0.36}$$

Calculate the square root of 0.36 and get 0.6.

$$\frac{3}{2}+\frac{1}{2}\times 0.6$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}+\frac{1}{2}\times \frac{3}{5}$$

Multiply \frac{1}{2} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{2}+\frac{1\times 3}{2\times 5}$$

Do the multiplications in the fraction \frac{1\times 3}{2\times 5}.

$$\frac{3}{2}+\frac{3}{10}$$

Least common multiple of 2 and 10 is 10. Convert \frac{3}{2} and \frac{3}{10} to fractions with denominator 10.

$$\frac{15}{10}+\frac{3}{10}$$

Since \frac{15}{10} and \frac{3}{10} have the same denominator, add them by adding their numerators.

$$\frac{15+3}{10}$$

Add 15 and 3 to get 18.

$$\frac{18}{10}$$

Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\frac{9}{5}$$

Factor

$$\frac{3 ^ {2}}{5} = 1\frac{4}{5} = 1.8$$