Problem 55 - Algebra and Trigonometry

Question

Rewrite each expression without absolute value bars. $$|\sqrt{2}-5|$$

Step-by-Step Solution

Answer

The expression \(|\sqrt{2} - 5|\) without absolute value bars is \(5 - \sqrt{2}\)

Step 1: Determine the Sign of the Expression Inside the Absolute Value

Notice that \(\sqrt{2}\) is less than 5, thus \(\sqrt{2} - 5\) is a negative number.

Step 2: Apply the Absolute Value Definition

Given that the expression is negative, by definition of absolute value, we 'negate' the expression to make it positive. Thus the expression without absolute value bars is \(-( \sqrt{2} - 5 )= 5 - \sqrt{2}\)