Practice Maths

Topic Review — Real Numbers — Solutions

Click any answer to watch the solution video.

  1. Classifying and converting real numbers

    1. Classifications:
    2. 0.&overline;27:
    3. 0.5&overline;4:
    4. Sets:

  2. Operations and rounding

    1. 0.048762 to 3 s.f.:
    2. 5499 to 2 s.f.:
    3. (3/5 + 1/4) × (2 − 7/8):
    4. 4.8² − 2.3×1.6:
    5. Ascending order:

  3. Surds — simplifying and operating

    1. √80:
    2. 3√12 − √27 + 2√3:
    3. 2√6 × 3√6:
    4. √5 × √45 − (√3)²:
    5. (2√7)² − √196:

  4. Estimating and ordering surds

    1. √40 bounds:
    2. Estimate √40:
    3. 5√2 vs 3√5:
    4. Ascending:
    5. √90 ≈ 9.5 check:

  5. Problem solving

    1. Square courtyard, area 75 m²:
    2. Triangle hypotenuses:
    3. √(a+b) vs √a + √b:
    4. Rectangle diagonal: