Math Quiz on Rational and Irrational Numbers
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Questions and Answers

Classify the number $\sqrt{7}$ as rational or irrational.

  • Neither
  • Both
  • Rational
  • Irrational (correct)
  • Estimate $\sqrt{2}$ to the nearest tenth.

  • 1.3
  • 1.6
  • 1.5
  • 1.4 (correct)
  • Solve the inequality $3x + 2 \leq 4x - \frac{3}{5}$.

  • $x \geq -\frac{3}{5}$ (correct)
  • $x \geq \frac{3}{5}$
  • $x \leq -\frac{3}{5}$
  • $x \leq \frac{3}{5}$
  • Simplify the expression $\sqrt{2}(1 - \sqrt{18})$.

    <p>$1 - 3\sqrt{2}$</p> Signup and view all the answers

    Compare $\sqrt{5}$ with $\frac{1}{2}$ using the symbols >, <, =.

    <p>$\sqrt{5} &gt; \frac{1}{2}$</p> Signup and view all the answers

    Arrange the numbers in ascending order: $\sqrt{7}$, $2.25$, $\sqrt{5}$.

    <p>2.25, $\sqrt{5}$, $\sqrt{7}$</p> Signup and view all the answers

    Study Notes

    Classifying Numbers

    • √25 and √16 are rational numbers
    • √7, √3, and √2 are irrational numbers

    Approximating Square Roots

    • Approximate √2 to the nearest tenth
    • Approximate -√3 to the nearest tenth
    • Simplify √6/√25 and approximate to the nearest tenth
    • Simplify √81/√49 and approximate to the nearest tenth

    Comparing Real Numbers

    • Compare √5 and 1/2
    • Compare 1.25 and √2.25
    • Compare √3/√9 and 0
    • Compare √12 and √20

    Ordering Numbers

    • Order √7, 2.25, and √5 from least to greatest
    • Order -3/5, -1, and -3.33 from least to greatest

    Solving Inequalities

    • Solve 3x + 2 ≤ 4x - 3/5
    • Solve 3/7z > 9/14
    • Solve 3y/8 ≥ 2
    • Solve 4m/11 < 22
    • Solve 6(z - 3) > 5(z + 1)
    • Solve 4(√1/2 + z/8) > 0

    Simplifying Expressions

    • Simplify √2(1-√18)
    • Simplify 3√12 + 2√3 - 4√3
    • Simplify (√7 - 8√7)/(2√7)
    • Simplify (6√44 + 18√11) / √5

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    Description

    This quiz assesses understanding of rational and irrational numbers, including square roots, comparisons, and ordering. Students will solve problems involving square roots, inequalities, and number lines.

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