Solve |2+3-3|/sqrt{2}

$$\frac { | 2 + 3 - 3 | } { \sqrt { 2 } }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Add 2 and 3 to get 5.

$$\frac{|5-3|}{\sqrt{2}}$$

Subtract 3 from 5 to get 2.

$$\frac{|2|}{\sqrt{2}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 2 is 2.

$$\frac{2}{\sqrt{2}}$$

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

$$\frac{2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$\sqrt{2}$$