Solve 1.15*(sqrt{2}*2.75-1.4div0.866div2)+1.441.4/0.886

$$1.15 \times ( \sqrt{ 2 } \times 2.75-1.4 \div 0.866 \div 2)+1.44 \frac{ 1.4 }{ 0.886 }$$

Evaluate

$$\frac{253\sqrt{2}}{80}+\frac{20050593}{9590950}\approx 6.56302463$$

Solution Steps

Express \frac{\frac{1.4}{0.866}}{2} as a single fraction.

$$1.15\left(2.75\sqrt{2}-\frac{1.4}{0.866\times 2}\right)+\frac{1.44\times 0.886+1.4}{0.886}$$

Multiply 0.866 and 2 to get 1.732.

$$1.15\left(2.75\sqrt{2}-\frac{1.4}{1.732}\right)+\frac{1.44\times 0.886+1.4}{0.886}$$

Expand \frac{1.4}{1.732} by multiplying both numerator and the denominator by 1000.

$$1.15\left(2.75\sqrt{2}-\frac{1400}{1732}\right)+\frac{1.44\times 0.886+1.4}{0.886}$$

Reduce the fraction \frac{1400}{1732} to lowest terms by extracting and canceling out 4.

$$1.15\left(2.75\sqrt{2}-\frac{350}{433}\right)+\frac{1.44\times 0.886+1.4}{0.886}$$

Use the distributive property to multiply 1.15 by 2.75\sqrt{2}-\frac{350}{433}.

$$3.1625\sqrt{2}+1.15\left(-\frac{350}{433}\right)+\frac{1.44\times 0.886+1.4}{0.886}$$

Convert decimal number 1.15 to fraction \frac{115}{100}. Reduce the fraction \frac{115}{100} to lowest terms by extracting and canceling out 5.

$$3.1625\sqrt{2}+\frac{23}{20}\left(-\frac{350}{433}\right)+\frac{1.44\times 0.886+1.4}{0.886}$$

Multiply \frac{23}{20} times -\frac{350}{433} by multiplying numerator times numerator and denominator times denominator.

$$3.1625\sqrt{2}+\frac{23\left(-350\right)}{20\times 433}+\frac{1.44\times 0.886+1.4}{0.886}$$

Do the multiplications in the fraction \frac{23\left(-350\right)}{20\times 433}.

$$3.1625\sqrt{2}+\frac{-8050}{8660}+\frac{1.44\times 0.886+1.4}{0.886}$$

Reduce the fraction \frac{-8050}{8660} to lowest terms by extracting and canceling out 10.

$$3.1625\sqrt{2}-\frac{805}{866}+\frac{1.44\times 0.886+1.4}{0.886}$$

Multiply 1.44 and 0.886 to get 1.27584.

$$3.1625\sqrt{2}-\frac{805}{866}+\frac{1.27584+1.4}{0.886}$$

Add 1.27584 and 1.4 to get 2.67584.

$$3.1625\sqrt{2}-\frac{805}{866}+\frac{2.67584}{0.886}$$

Expand \frac{2.67584}{0.886} by multiplying both numerator and the denominator by 100000.

$$3.1625\sqrt{2}-\frac{805}{866}+\frac{267584}{88600}$$

Reduce the fraction \frac{267584}{88600} to lowest terms by extracting and canceling out 8.

$$3.1625\sqrt{2}-\frac{805}{866}+\frac{33448}{11075}$$

Least common multiple of 866 and 11075 is 9590950. Convert -\frac{805}{866} and \frac{33448}{11075} to fractions with denominator 9590950.

$$3.1625\sqrt{2}-\frac{8915375}{9590950}+\frac{28965968}{9590950}$$

Since -\frac{8915375}{9590950} and \frac{28965968}{9590950} have the same denominator, add them by adding their numerators.

$$3.1625\sqrt{2}+\frac{-8915375+28965968}{9590950}$$

Add -8915375 and 28965968 to get 20050593.

$$3.1625\sqrt{2}+\frac{20050593}{9590950}$$

Factor

$$\frac{242651035 \sqrt{2} + 160404744}{76727600} = 6.563024630261713$$