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AQA Maths 9-1 (Grade 5 topics (Surds (Example questions: 1) √48 + √12…

- - - - 1)
        48 = 4 x 12
        4 = 2 x 2= 2
        12 = 4 x 3
        4 = 2 x 2 = 2
        2 x 2 x √3 = 4√3
        12 = 4 x 3
        4 = 2 x 2
        2√3
        27 = 9 x 3
        9= 3 x 3
        3√3
        2√3 + 4√3 + 3√3 = 9√3
        2)
        8 = 2 x 2 x 2 = 2√2
        18= 9 x 2 = 3 x 2 = 3√2
        2√2 + 3√2 = 5√2
        3)
        20 = 10 x 2 = 5 x 2 = 2√5
        45 = 9 x 5 =3 x 5 = 3√5
        2√5 + 3√5 = 5√5
  - - - an example of HCF between 24 and 18 is:
        18 = 3 6 2 9
        24 = 4 6 2 12
        the HCF would be 6
    - - an example of an LCM is the LCM between 3 and 7:
        3 6 9 12 15 18 21 23 27 30 33 36 39 42
        7 14 21 28 35 42
        the LCM would be 42
  - - - Then you can swap them around if necessary to avoid a negative number
        
        Then you divide the resulting y by the number to get your y value which you can then substitute into the equation
  - - - If they are on a number line, there are two types of circles that are place on the line, either a fully black circle or a white circle with a black outline
        
        When the circle is white but with a black outline, it means that the numbers following/ before the circle are less than or more than but not equal to
        
        When the circle is black, it means that the following numbers can be equal to / less than or more than
      - If they are put in an equation they look like this:
        x > 5 or 2<x≥5
      - To work out inequalities you have to make both sides have one component in them, in which you can then substitute it into a number line