6 Questions
Classify the number $\sqrt{7}$ as rational or irrational.
Irrational
Estimate $\sqrt{2}$ to the nearest tenth.
1.4
Solve the inequality $3x + 2 \leq 4x - \frac{3}{5}$.
$x \geq -\frac{3}{5}$
Simplify the expression $\sqrt{2}(1 - \sqrt{18})$.
$1 - 3\sqrt{2}$
Compare $\sqrt{5}$ with $\frac{1}{2}$ using the symbols >, <, =.
$\sqrt{5} > \frac{1}{2}$
Arrange the numbers in ascending order: $\sqrt{7}$, $2.25$, $\sqrt{5}$.
2.25, $\sqrt{5}$, $\sqrt{7}$
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
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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