Solve sqrt{0,64:4}-0,3*sqrt{1-3/4}+3/2=

$$\sqrt { 0,64 : 4 } - 0,3 \cdot \sqrt { 1 - \frac { 3 } { 4 } } + \frac { 3 } { 2 } =$$

Evaluate

$$1,75$$

Solution Steps

Expand \frac{0,64}{4} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{64}{400}}-0,3\sqrt{1-\frac{3}{4}}+\frac{3}{2}$$

Reduce the fraction \frac{64}{400} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{4}{25}}-0,3\sqrt{1-\frac{3}{4}}+\frac{3}{2}$$

Rewrite the square root of the division \frac{4}{25} as the division of square roots \frac{\sqrt{4}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{2}{5}-0,3\sqrt{1-\frac{3}{4}}+\frac{3}{2}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{2}{5}-0,3\sqrt{\frac{4}{4}-\frac{3}{4}}+\frac{3}{2}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{5}-0,3\sqrt{\frac{4-3}{4}}+\frac{3}{2}$$

Subtract 3 from 4 to get 1.

$$\frac{2}{5}-0,3\sqrt{\frac{1}{4}}+\frac{3}{2}$$

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.

$$\frac{2}{5}-0,3\times \frac{1}{2}+\frac{3}{2}$$

Convert decimal number 0,3 to fraction \frac{3}{10}.

$$\frac{2}{5}-\frac{3}{10}\times \frac{1}{2}+\frac{3}{2}$$

Multiply \frac{3}{10} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}-\frac{3\times 1}{10\times 2}+\frac{3}{2}$$

Do the multiplications in the fraction \frac{3\times 1}{10\times 2}.

$$\frac{2}{5}-\frac{3}{20}+\frac{3}{2}$$

Least common multiple of 5 and 20 is 20. Convert \frac{2}{5} and \frac{3}{20} to fractions with denominator 20.

$$\frac{8}{20}-\frac{3}{20}+\frac{3}{2}$$

Since \frac{8}{20} and \frac{3}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-3}{20}+\frac{3}{2}$$

Subtract 3 from 8 to get 5.

$$\frac{5}{20}+\frac{3}{2}$$

Reduce the fraction \frac{5}{20} to lowest terms by extracting and canceling out 5.

$$\frac{1}{4}+\frac{3}{2}$$

Least common multiple of 4 and 2 is 4. Convert \frac{1}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{1}{4}+\frac{6}{4}$$

Since \frac{1}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{1+6}{4}$$

Add 1 and 6 to get 7.

$$\frac{7}{4}$$

Factor

$$\frac{7}{2 ^ {2}} = 1\frac{3}{4} = 1.75$$