Multiple choice

If the value of the expression $\displaystyle \frac { x-12 }{ \sqrt { 8 } } $ can be approximated to be equal to $\displaystyle \frac { x\sqrt { 2 } }{ 4 } -C$, then determine the value of $C$ in the equation.

  1. $-3$
  2. $\displaystyle -\sqrt { 3 } $
  3. $2$
  4. $\displaystyle 3\sqrt { 2 } $
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D Correct answer
Explanation

(x-12)/sqrt(8) = (x-12)/(2*sqrt(2)) = x/(2*sqrt(2)) - 12/(2*sqrt(2)) = x*sqrt(2)/4 - 6/sqrt(2) = x*sqrt(2)/4 - 3*sqrt(2). Comparing with x*sqrt(2)/4 - C, we get C = 3*sqrt(2).

AI explanation

Rationalize the denominator of the first fraction by multiplying both the numerator and the denominator by the square root of 2. The denominator becomes the square root of 16, which is 4, so the expression becomes (x minus 12) times the square root of 2, all divided by 4. Distributing the square root of 2 gives (x times the square root of 2) divided by 4 minus 12 times the square root of 2 divided by 4, which simplifies to (x times the square root of 2) divided by 4 minus 3 times the square root of 2. Matching this to the given form shows that C is 3 times the square root of 2.

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