2^(1/2)/4 + 3/(2*2^(1/2)) =

Question

\frac{\sqrt{2}}{4} + \frac{3}{2\sqrt{2}} = A. \frac{\sqrt{2}}{2} B. \frac{3\sqrt{2}}{2} C. \sqrt{2} D. 2\sqrt{2} E. 3\sqrt{2} 2024-01-24_21-41-33.png

Bunuel · Accepted Answer

\frac{\sqrt{2}}{4} + \frac{3}{2\sqrt{2}} =

=\frac{\sqrt{2}}{4} + \frac{3}{2\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}} =

=\frac{\sqrt{2}}{4} + \frac{3\sqrt{2}}{4} =

=\frac{4\sqrt{2}}{4} =

=\sqrt{2}

Answer: C.

gmatophobia · Answer

\frac{\sqrt{2}}{4} + \frac{3}{2\sqrt{2}} =

\frac{(2*\sqrt{2}*\sqrt{2})+(3 * 4)}{8\sqrt{2}}

\frac{2*2)+(3 * 4)}{8\sqrt{2}}

\frac{16}{8\sqrt{2}}

\frac{2}{\sqrt{2}}

\sqrt{2}

Option C

phil2804 · Answer

Hey, 
why is it not possible to square everything having:

(2/16) + (9/8)

getting everything onto the same denominator: 2/16 + 18/16 = 20/16 and then taking the root?

What is my mistake?

Bunuel · Answer

Because (a + b)^2 equals a^2 + 2ab + b^2, not a^2 + b^2.

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