Solve 245+1.833(35/sqrt{10})

$$245 + 1.833 ( \frac { 35 } { \sqrt { 10 } } )$$

Evaluate

$$\frac{12831\sqrt{10}}{2000}+245\approx 265.287592329$$

Solution Steps

Rationalize the denominator of \frac{35}{\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$245+1.833\times \frac{35\sqrt{10}}{\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$245+1.833\times \frac{35\sqrt{10}}{10}$$

Divide 35\sqrt{10} by 10 to get \frac{7}{2}\sqrt{10}.

$$245+1.833\times \frac{7}{2}\sqrt{10}$$

Convert decimal number 1.833 to fraction \frac{1833}{1000}.

$$245+\frac{1833}{1000}\times \frac{7}{2}\sqrt{10}$$

Multiply \frac{1833}{1000} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$245+\frac{1833\times 7}{1000\times 2}\sqrt{10}$$

Do the multiplications in the fraction \frac{1833\times 7}{1000\times 2}.

$$245+\frac{12831}{2000}\sqrt{10}$$

Factor

$$\frac{7 {(1833 \sqrt{10} + 70000)}}{2000} = 265.28759232881026$$