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Estimating Roots and Irrational Numbers: Classroom Packet

Grade 8 Algebra: Estimating Roots and Irrational Numbers

Name: ______________________Date: ____________Score: ____ / 8

Level 1

Between two whole numbers

  1. 1. Name the two whole numbers it lies between:
    5\sqrt{5}
  2. 2. Name the two whole numbers it lies between:
    10\sqrt{10}
  3. 3. Name the two whole numbers it lies between:
    20\sqrt{20}
  4. 4. Name the two whole numbers it lies between:
    30\sqrt{30}
  5. 5. Name the two whole numbers it lies between:
    45\sqrt{45}
  6. 6. Name the two whole numbers it lies between:
    60\sqrt{60}
  7. 7. Name the two whole numbers it lies between:
    75\sqrt{75}
  8. 8. Name the two whole numbers it lies between:
    90\sqrt{90}

Answer Key

Level 1

  1. 1. 2 and 32 \text{ and } 3
  2. 2. 3 and 43 \text{ and } 4
  3. 3. 4 and 54 \text{ and } 5
  4. 4. 5 and 65 \text{ and } 6
  5. 5. 6 and 76 \text{ and } 7
  6. 6. 7 and 87 \text{ and } 8
  7. 7. 8 and 98 \text{ and } 9
  8. 8. 9 and 109 \text{ and } 10

Grade 8 Algebra: Estimating Roots and Irrational Numbers

Name: ______________________Date: ____________Score: ____ / 8

Level 2

Nearest whole number

  1. 1. Estimate to the nearest whole number:
    8\sqrt{8}
  2. 2. Estimate to the nearest whole number:
    15\sqrt{15}
  3. 3. Estimate to the nearest whole number:
    26\sqrt{26}
  4. 4. Estimate to the nearest whole number:
    40\sqrt{40}
  5. 5. Estimate to the nearest whole number:
    50\sqrt{50}
  6. 6. Estimate to the nearest whole number:
    63\sqrt{63}
  7. 7. Estimate to the nearest whole number:
    80\sqrt{80}
  8. 8. Estimate to the nearest whole number:
    99\sqrt{99}

Answer Key

Level 2

  1. 1. 33
  2. 2. 44
  3. 3. 55
  4. 4. 66
  5. 5. 77
  6. 6. 88
  7. 7. 99
  8. 8. 1010

Grade 8 Algebra: Estimating Roots and Irrational Numbers

Name: ______________________Date: ____________Score: ____ / 8

Level 3

Rational or irrational, and ordering

  1. 1. Rational or irrational?:
    49\sqrt{49}
  2. 2. Rational or irrational?:
    12\sqrt{12}
  3. 3. Rational or irrational?:
    273\sqrt[3]{27}
  4. 4. Rational or irrational?:
    π\pi
  5. 5. Rational or irrational?:
    916\sqrt{\tfrac{9}{16}}
  6. 6. Order from least to greatest:
    10,  3.5,  π\sqrt{10},\; 3.5,\; \pi
  7. 7. Order from least to greatest:
    50,  7.2,  48\sqrt{50},\; 7.2,\; \sqrt{48}
  8. 8. Estimate to one decimal place:
    30\sqrt{30}

Answer Key

Level 3

  1. 1. rational\text{rational}
  2. 2. irrational\text{irrational}
  3. 3. rational\text{rational}
  4. 4. irrational\text{irrational}
  5. 5. rational\text{rational}
  6. 6. π,  10,  3.5\pi,\; \sqrt{10},\; 3.5
  7. 7. 48,  50,  7.2\sqrt{48},\; \sqrt{50},\; 7.2
  8. 8. ≈5.5\approx 5.5