Multiple choice

Find the approximate value of $\displaystyle\frac{1+\sqrt{0.01}}{1-\sqrt{0.1}}$.

  1. $0.6$
  2. $1.1$
  3. $1.6$
  4. $1.7$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Numerator = 1 + sqrt(0.01) = 1 + 0.1 = 1.1. Denominator = 1 - sqrt(0.1) approx 1 - 0.316 = 0.684. 1.1 / 0.684 approx 1.608.

AI explanation

First, calculate the square roots to find $\sqrt{0.01} = 0.1$ and $\sqrt{0.1} \approx 0.316$. Substituting these into the original fraction gives $\frac{1 + 0.1}{1 - 0.316}$, which simplifies to $\frac{1.1}{0.684}$. Dividing $1.1$ by $0.684$ yields approximately $1.608$, which rounds to $1.6$.

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