Problem Solving

If x ≠ 0, then √(x²)/x =

A) -1
B) 0
C) 1
D) x
E) |x|/x

Quick solution: √(x²) is EQUIVALENT to |x|
So, √(x²)/x = |x|/x = E

If x ≠ 0, then (√x²)/x =

A) -1
B) 0
C) 1
D) x
E) |x|/x

Longer solution:

TEST some numbers.

Let x = 2
This means √(x²)/x = √(2²)/2 = (√4)/2 = 2/2 = 1
Now check the answer choices:

A) -1 NOPE. ELIMINATE
B) 0 NOPE. ELIMINATE
C) 1 Yes. KEEP
D) x NOPE. x = 2 but our expression evaluated to 1. ELIMINATE
E) |x|/x. If x = 2, |x|/x = |2|/2 = 1 KEEP

We're left with C and E.
Now TEST another value.

Let x = -2
This means √(x²)/x = √[(-2)²]/-2 = (√4)/-2 = 2/-2 = -1
Now check the answer choices:
C) 1 NOPE. ELIMINATE

We're left with E, so it must be correct.