Which of the following is equal to 24/3 2^1/2 - 4/2^1/2

Question

Which of the following is equal to  \frac{24}{3 \sqrt{2}} - \frac{4}{\sqrt{2}}

(A)  \sqrt{25}

(B) 4

(C)  2 \sqrt{2}

(D)  3 \sqrt{3}

(E)  \sqrt{36}

BrentGMATPrepNow · Accepted Answer

Given:  \frac{24}{3 \sqrt{2}} - \frac{4}{\sqrt{2}}

For the first fraction, multiply numerator and denominator by  \sqrt{2}  to get:  \frac{24\sqrt{2}}{6} - \frac{4}{\sqrt{2}}

For the second fraction, multiply numerator and denominator by  3\sqrt{2}  to get:  \frac{24\sqrt{2}}{6} - \frac{12\sqrt{2}}{6}

Combine fractions: \frac{12\sqrt{2}}{6}

Simplify:  2\sqrt{2}

Answer: C

Cheers, 
Brent

CrackverbalGMAT · Answer

The expression  \frac{24}{3\sqrt{2}} - \frac{4}{\sqrt{2}} = \frac{8}{\sqrt{2}} - \frac{4}{\sqrt{2}} = \frac{4}{\sqrt{2}}

Multiplying and dividing by  \sqrt{2} , we get  \frac{4\sqrt{2}}{\sqrt{2} * \sqrt{2}} = \frac{4\sqrt{2}}{2} = 2\sqrt{2}

Option C

Arun Kumar

Abhishek009 · Answer

\frac{24}{3 \sqrt{2}} - \frac{4}{\sqrt{2}}

=  \frac{24 - 12}{3 \sqrt{2}}

=  \frac{12}{3 \sqrt{2}}

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

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

=  2 \sqrt{2} , Answer must be (C)

ablatt4 · Answer

Multiply both denominators and numerators by sqrt 2 and clear the root in the denominators

(24 sqrt 2) / 6 - (4 sqrt 2) / 2

simplify for common denominator

8 sqrt 2 -4 sqrt 2 / 2

4sqrt 2 / 2

2 sqrt 2

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