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Level 5-6 Numbers - Roots
A square, like these tiles, of area 169 cm square has side length of how many centimetres? See question 4 to find out. (Picture courtesy of snigl3t at Flickr)

Level 5-6 Numbers - Roots

In the study of Maths, a number multiplied by itself creates its own square. The original number is called the square root of the new number. Finding square and cube roots are useful calculations with the same priority as Index in the BIDMAS order.

  1. Which of these is not a way of writing the square root of 625?
    3 - The square root of 125 is 11.18 to two decimal places.
  2. The square root of 425 lies between .......
    2 - 202 = 400; 212 = 441; √425 = 20.61552813.......
  3. The cube root of 216 is .......
    1 - Since 162 = 256, 163 must be bigger and 263 or 363 will be bigger still, so 6 is the only sensible answer
  4. A square of area 169 cm2 has side length .......
    4 - √169 = 13
  5. A cube of volume 1,000 cm3 has side length .......
    2 - ∛1,000 = 10
  6. What is the square root of 54?
    2 - To find the square root of a power number you divide the index by 2. √(54) = 52
  7. What is the square root of 64 x 144?
    1 - The square root of a product is the product of the square roots.√64 x √144 = 8 x 12
  8. What is the cube root of 79?
    3 - To find the cube root of a power number you divide the index by 3. ∛(79) = 73
  9. The square with the same area as a rectangle measuring 9 cm by 16 cm has side length .......
    3 - 9 x 16 = 144; √144 = 12
  10. What is the total surface area of a cube which has a volume of 729 cm3?
    4 - ∛729 = 9 so each square face has an area of 81 cm2. A cube has six square faces; 6 x 81 = 486

Author: Frank Evans

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