What are surds and why are they used?

Surds are irrational numbers that can't be represented accurately as a fraction or reccuring decimal, so they are left as a square root. For example:  √  3 . Calculate the square root of 3 using your calculator, rounded to 3dp the answer is 1.732. Now square 1.732 and the answer shown on your calculator is 2.999824 which doesn't equal 3. However, if you use the surd √ 3 instead of the decimal 1.732 you get the exact answer. Put (√  3 )²  into your calculator and the answer will be 3. This shows how surds are more accurate and using a rounded decimal instead will cause rounding errors, as seen in the first calculation. Surds are used in real life to make sure that important calculations are precise, for example by engineers building bridges.