Solve 2.021*3/2sqrt{1-0.52/50-2}

$$2.021 \times \frac{ 3 }{ 2 } \sqrt{ \frac{ 1-0.52 }{ 50-2 } }$$

Evaluate

$$0.30315$$

Solution Steps

Convert decimal number 2.021 to fraction \frac{2021}{1000}.

$$\frac{2021}{1000}\times \frac{3}{2}\sqrt{\frac{1-0.52}{50-2}}$$

Multiply \frac{2021}{1000} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2021\times 3}{1000\times 2}\sqrt{\frac{1-0.52}{50-2}}$$

Do the multiplications in the fraction \frac{2021\times 3}{1000\times 2}.

$$\frac{6063}{2000}\sqrt{\frac{1-0.52}{50-2}}$$

Subtract 0.52 from 1 to get 0.48.

$$\frac{6063}{2000}\sqrt{\frac{0.48}{50-2}}$$

Subtract 2 from 50 to get 48.

$$\frac{6063}{2000}\sqrt{\frac{0.48}{48}}$$

Expand \frac{0.48}{48} by multiplying both numerator and the denominator by 100.

$$\frac{6063}{2000}\sqrt{\frac{48}{4800}}$$

Reduce the fraction \frac{48}{4800} to lowest terms by extracting and canceling out 48.

$$\frac{6063}{2000}\sqrt{\frac{1}{100}}$$

Rewrite the square root of the division \frac{1}{100} as the division of square roots \frac{\sqrt{1}}{\sqrt{100}}. Take the square root of both numerator and denominator.

$$\frac{6063}{2000}\times \frac{1}{10}$$

Multiply \frac{6063}{2000} times \frac{1}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6063\times 1}{2000\times 10}$$

Do the multiplications in the fraction \frac{6063\times 1}{2000\times 10}.

$$\frac{6063}{20000}$$

Factor

$$\frac{3 \cdot 43 \cdot 47}{2 ^ {5} \cdot 5 ^ {4}} = 0.30315$$