Solve (-28.57divsqrt{2})+(18divsqrt{2})

$$(-28.57 \div \sqrt{ 2 } )+(18 \div \sqrt{ 2 } )$$

Evaluate

$$-\frac{1057\sqrt{2}}{200}\approx -7.474118677$$

Solution Steps

Rationalize the denominator of \frac{-28.57}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-28.57\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\frac{18}{\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-28.57\sqrt{2}}{2}+\frac{18}{\sqrt{2}}$$

Divide -28.57\sqrt{2} by 2 to get -14.285\sqrt{2}.

$$-14.285\sqrt{2}+\frac{18}{\sqrt{2}}$$

Rationalize the denominator of \frac{18}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$-14.285\sqrt{2}+\frac{18\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-14.285\sqrt{2}+\frac{18\sqrt{2}}{2}$$

Divide 18\sqrt{2} by 2 to get 9\sqrt{2}.

$$-14.285\sqrt{2}+9\sqrt{2}$$

Combine -14.285\sqrt{2} and 9\sqrt{2} to get -5.285\sqrt{2}.

$$-5.285\sqrt{2}$$