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Class 9 Maths — Surds and real numbers

Simplify, add and multiply surds, use fractional powers, and clear a surd out of a denominator.

Name: ________________________

  1. 1.Work each expression out, then sort it by whether the result is rational or irrational.

    Groups: Rational · Irrational

    • √5 × √5
    • √3 + √3
    • √2 × √8
    • √2 × √3
    • 2 + √7
    • √6 × √6

  2. 2.Which of these is equal to 16 to the power 1/2?

    • a) 8
    • b) 32
    • c) 4
    • d) 256

  3. 3.What is √3 × √12?

  4. 4.What is 8 to the power 2/3?

  5. 5.What is √5 × √5?

  6. 6.What is (√6 + √5)(√6 - √5)?

  7. 7.Put these numbers in order, smallest first.

    • √2
    • √5
    • 3
    • √11

  8. 8.Match each surd to its simplest form.

    • √12
    • √18
    • √75
    • √32
    • √45
    • 2√3
    • 3√5
    • 5√3
    • 3√2
    • 4√2

Answer key — Class 9 Maths — Surds and real numbers

  1. 1. √2 × √8 → Rational; √3 + √3 → Irrational; √5 × √5 → Rational; 2 + √7 → Irrational; √6 × √6 → Rational; √2 × √3 → Irrational
  2. 2. c) 4
  3. 3. 6
  4. 4. 4
  5. 5. 5
  6. 6. 1
  7. 7. 1. √2 2. √5 3. 3 4. √11
  8. 8. √12 → 2√3; √18 → 3√2; √75 → 5√3; √32 → 4√2; √45 → 3√5