Questions: Select the correct choice that completes the sentence below. A quotient is considered rationalized if its denominator contains no square

Select the correct choice that completes the sentence below. A quotient is considered rationalized if its denominator contains no square

Transcript text: Select the correct choice that completes the sentence below. A quotient is considered rationalized if its denominator contains no $\square$

Solution

Solution Steps

Step 1: Identify the Expression

We start with the expression $ \frac{1}{\sqrt{2}} $. The goal is to rationalize the denominator, which currently contains a square root.

Step 2: Multiply by the Conjugate

To eliminate the square root from the denominator, we multiply both the numerator and the denominator by $ \sqrt{2} $: \[ \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{1 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{\sqrt{2}}{2} \]

Step 3: Simplify the Expression

The denominator simplifies as follows: \[ \sqrt{2} \cdot \sqrt{2} = 2 \] Thus, the rationalized expression is: \[ \frac{\sqrt{2}}{2} \]