Surds (maths revision) Higher

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Basic Rules

A surd is a squre root which cannot be reduce to a whole number. For example, 4 sqpare roots = 2 is not a surd, because the answer is a wholel number. But 5 square roots is not a whole number. You could use a calcultor to find out the square roots of 5 is 2.236067977.. but instead of this we leave the answers in the square root form, as a surd.

You'll need to be able to simplify expressions involving surds. Here are some genaral rules.

square root of ab = square root of a x square root of b (http://www.bbc.co.uk/staticarchive/c6067d8ff3a7da7fc8e2f45c2d6672d8190e7fae.png)

square root of a x square root of a = a (http://www.bbc.co.uk/staticarchive/9d95f4688d979d20ddbe7946bd957ae923a5bf26.png)

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Test yourself (Question 1)

Simplifly the squre root of 12

  • use the general rules
  • square root of ab = square root of a x square root of b (http://www.bbc.co.uk/staticarchive/c6067d8ff3a7da7fc8e2f45c2d6672d8190e7fae.png)

  • square root of 12 (http://www.bbc.co.uk/staticarchive/8f9c8007d6bd2a20bb7987efa820d7657ea37b82.png)= square root of 4 x square root of 3 (http://www.bbc.co.uk/staticarchive/838e2ccc14bf97e6bfbaa72b105669abff6170c9.png)2 square root of 3 (http://www.bbc.co.uk/staticarchive/774f961c9ae7a46891d85f4b64654d8d915eb46e.png)  
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Test yourself (Question 2)

Simplifysquare root of 12 x square root of 3 (http://www.bbc.co.uk/staticarchive/e1de118473f2b807846bf3d826e837d7f820393a.png)

  • use the general rules
  • square root of a x square root of a = a (http://www.bbc.co.uk/staticarchive/9d95f4688d979d20ddbe7946bd957ae923a5bf26.png)
  • square root of 12 x square root of 3 (http://www.bbc.co.uk/staticarchive/e1de118473f2b807846bf3d826e837d7f820393a.png) = square root of (12 x 3) (http://www.bbc.co.uk/staticarchive/0b42712e7125d57794605e9ad0191392818c6c94.png) = square root of 36 (http://www.bbc.co.uk/staticarchive/811b731c2d66a7f52f0392fdf0fc85370c3106fd.png) = 6

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Test yourself (Question 3)

Simplifysquare root of 12 over square root of 6 (http://www.bbc.co.uk/staticarchive/143345f95bc2de27352120f74a86925505a8a610.png)

  • use general rules (in general square root of a over square root of b = square root of a over b) (http://www.bbc.co.uk/staticarchive/e3a879fb87b683a7c937a3aae273b6cddf2a03b6.png)
  • square root of 12 over square root of 6 (http://www.bbc.co.uk/staticarchive/143345f95bc2de27352120f74a86925505a8a610.png)= square root of 12 over 6 (http://www.bbc.co.uk/staticarchive/d88a589977637835ad775b6530bbf8e885ef19ec.png)  square root of 2 (http://www.bbc.co.uk/staticarchive/1152219803439d63e3e9127d9c2a637aa627e0ac.png)

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