Solve 3sqrt{16}-219+18/sqrt{2}

$$3 \sqrt { 16 } - 219 + \frac { 18 } { \sqrt { 2 } }$$

Evaluate

$$9\left(\sqrt{2}-23\right)\approx -194.272077939$$

Solution Steps

Calculate the square root of 16 and get 4.

$$3\times 4-219+\frac{18}{\sqrt{2}}$$

Multiply 3 and 4 to get 12.

$$12-219+\frac{18}{\sqrt{2}}$$

Subtract 219 from 12 to get -207.

$$-207+\frac{18}{\sqrt{2}}$$

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

$$-207+\frac{18\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-207+\frac{18\sqrt{2}}{2}$$

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

$$-207+9\sqrt{2}$$

Factor

$$9 {(\sqrt{2} - 23)} = -194.272077939$$