Problem 55 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: Check the Value Inside the Absolute Value

The first step is to look at the number inside the absolute value bars \(|\sqrt{2}-5|\). We see that \(\sqrt{2}-5 < 0\) because the square root of 2 is approximately 1.414, and when you subtract 5 from that you get a negative number.

Step 2: Apply the Absolute Value Definition

Since we determined that the number inside the absolute value bars is negative, the absolute value of the number will be the negative of the number. Therefore, \(|\sqrt{2} - 5|\) will be \(-( \sqrt{2} - 5)\).

Step 3: Simplify the Expression

By distributing the negative sign, the expression simplifies to \(5 - \sqrt{2}\).