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Year 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.What is √5 × √5?

  2. 2.What is (√6 + √5)(√6 - √5)?

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

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

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

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

  5. 5.3√7 + 4√7 can be written as a√7. What is a?

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

    • √5
    • 3
    • √2
    • √11

  7. 7.What is √3 × √12?

  8. 8.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?

Answer key — Year 9 Maths — Surds and real numbers

  1. 1. 5
  2. 2. 1
  3. 3. d) √(ab)
  4. 4. d) 4
  5. 5. 7
  6. 6. 1. √2 2. √5 3. 3 4. √11
  7. 7. 6
  8. 8. 5