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Lesson 4: Approximating Square Roots — Practice Questions

  1. 1. Convert the repeating decimal $0.\overline{5}$ to a fraction in simplest form. The fraction is ___.

  2. 2. To convert $x = 0.\overline{18}$ to a fraction, what is the resulting equation after multiplying by the correct power of 10 and subtracting the original equation?

    • A. $9x = 18$
    • B. $99x = 18$
    • C. $90x = 18$
    • D. $99x = 1.8$
  3. 3. Express the repeating decimal $0.\overline{54}$ as a fraction in its simplest form. The fraction is ___.

  4. 4. Convert the decimal $0.4\overline{8}$ to a fraction in simplest form. The fraction is ___.

  5. 5. To convert the decimal $0.12\overline{3}$ to a fraction, which two equations should you subtract to eliminate the repeating part?

    • A. Subtract $x$ from $100x$
    • B. Subtract $10x$ from $100x$
    • C. Subtract $100x$ from $1000x$
    • D. Subtract $10x$ from $1000x$
  6. 6. The irrational number $\sqrt{85}$ lies between which two consecutive integers?

    • A. 7 and 8
    • B. 8 and 9
    • C. 9 and 10
    • D. 10 and 11
  7. 7. Given that $7.0^2 = 49$ and $7.1^2 = 50.41$, what is the best approximation of $\sqrt{50}$ to one decimal place? ___

  8. 8. Which inequality correctly compares the numbers $\sqrt{15}$ and $3.8$?

    • A. $\sqrt{15} < 3.8$
    • B. $\sqrt{15} > 3.8$
    • C. $\sqrt{15} = 3.8$
    • D. Cannot be determined
  9. 9. A square garden has an area of 800 square meters. Which of the following is the best approximation for the length of one side of the garden?

    • A. 28.1 m
    • B. 28.3 m
    • C. 28.5 m
    • D. 28.7 m
  10. 10. Approximations for $\sqrt{40}$ are tested. It is known that $6.3^2 = 39.69$ and $6.4^2 = 40.96$. The better approximation is ___.