Solve sqrt{(3+3/4):sqrt{(3/5-9/25)*sqrt{4-7/4}}}=

$$\sqrt { ( 3 + \frac { 3 } { 4 } ) : \sqrt { ( \frac { 3 } { 5 } - \frac { 9 } { 25 } ) \times \sqrt { 4 - \frac { 7 } { 4 } } } } =$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Convert 3 to fraction \frac{12}{4}.

$$\sqrt{\frac{\frac{12}{4}+\frac{3}{4}}{\sqrt{\left(\frac{3}{5}-\frac{9}{25}\right)\sqrt{4-\frac{7}{4}}}}}$$

Since \frac{12}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{\frac{12+3}{4}}{\sqrt{\left(\frac{3}{5}-\frac{9}{25}\right)\sqrt{4-\frac{7}{4}}}}}$$

Add 12 and 3 to get 15.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\left(\frac{3}{5}-\frac{9}{25}\right)\sqrt{4-\frac{7}{4}}}}}$$

Least common multiple of 5 and 25 is 25. Convert \frac{3}{5} and \frac{9}{25} to fractions with denominator 25.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\left(\frac{15}{25}-\frac{9}{25}\right)\sqrt{4-\frac{7}{4}}}}}$$

Since \frac{15}{25} and \frac{9}{25} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{15-9}{25}\sqrt{4-\frac{7}{4}}}}}$$

Subtract 9 from 15 to get 6.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{6}{25}\sqrt{4-\frac{7}{4}}}}}$$

Convert 4 to fraction \frac{16}{4}.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{6}{25}\sqrt{\frac{16}{4}-\frac{7}{4}}}}}$$

Since \frac{16}{4} and \frac{7}{4} have the same denominator, subtract them by subtracting their numerators.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{6}{25}\sqrt{\frac{16-7}{4}}}}}$$

Subtract 7 from 16 to get 9.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{6}{25}\sqrt{\frac{9}{4}}}}}$$

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.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{6}{25}\times \frac{3}{2}}}}$$

Multiply \frac{6}{25} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{6\times 3}{25\times 2}}}}$$

Do the multiplications in the fraction \frac{6\times 3}{25\times 2}.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{18}{50}}}}$$

Reduce the fraction \frac{18}{50} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{\frac{15}{4}}{\sqrt{\frac{9}{25}}}}$$

Rewrite the square root of the division \frac{9}{25} as the division of square roots \frac{\sqrt{9}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\sqrt{\frac{\frac{15}{4}}{\frac{3}{5}}}$$

Divide \frac{15}{4} by \frac{3}{5} by multiplying \frac{15}{4} by the reciprocal of \frac{3}{5}.

$$\sqrt{\frac{15}{4}\times \frac{5}{3}}$$

Multiply \frac{15}{4} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\sqrt{\frac{15\times 5}{4\times 3}}$$

Do the multiplications in the fraction \frac{15\times 5}{4\times 3}.

$$\sqrt{\frac{75}{12}}$$

Reduce the fraction \frac{75}{12} to lowest terms by extracting and canceling out 3.

$$\sqrt{\frac{25}{4}}$$

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

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$