← Back to the activity

Year 10 Maths — Surds and real numbers

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

Name: ________________________

  1. 1.What is 27 to the power 1/3?

  2. 2.√50 can be written as a√2. What is a?

  3. 3.What is √3 × √12?

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

    Groups: Rational · Irrational

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

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

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

    • √2
    • 3
    • √11
    • √5

  7. 7.To clear the surd from the denominator of 1/√5, multiply top and bottom by √5. The result is √5 over b. What is b?

  8. 8.For positive real numbers a and b, √a × √b is always equal to...

    • a) √a + √b
    • b) √(ab)
    • c) a√b
    • d) √(a + b)

Answer key — Year 10 Maths — Surds and real numbers

  1. 1. 3
  2. 2. 5
  3. 3. 6
  4. 4. √2 × √8 → Rational; √3 + √3 → Irrational; √5 × √5 → Rational; 2 + √7 → Irrational; √6 × √6 → Rational; √2 × √3 → Irrational
  5. 5. 4
  6. 6. 1. √2 2. √5 3. 3 4. √11
  7. 7. 5
  8. 8. b) √(ab)