GMAT Practice Question: \frac{\sqrt{2}}{4}+\frac{3}{2 \sqrt{2}}=
Question
\frac{\sqrt{2}}{4}+\frac{3}{2 \sqrt{2}}=
- \frac{\sqrt{2}}{2}
- \frac{3 \sqrt{2}}{2}
- \sqrt{2}
- 2 \sqrt{2}
- 3 \sqrt{2}
Topics: fractions, roots
Solution
Step 1
We simplify the second fraction by rationalizing the denominator
\frac{3}{2\sqrt{2}} = \frac{3}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{2\times2} = \frac{3\sqrt{2}}{4}
Step 2
We add the two like terms over the common denominator
\frac{\sqrt{2}}{4} + \frac{3\sqrt{2}}{4} = \frac{4\sqrt{2}}{4} = \sqrt{2}
Answer
C
