11 Mar 2013

Maths Help: Square Roots, Basic Surds

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What is a square root? √ is 'square root of': the way my son explained it is 'they're the opposite of squaring a number'.

A maths teacher might say it's 'the inverse operation' (opposite) of raising a number to a power.
3 x 3 = 3² = 9

√9 = 3

How can I find the square root of 81 or any other number?
81 is easy, because we learned the sequence (set):

1²  2²  3²  4²   5²    6²    7²    8²   9²    10²    11²    12²
2   4   9   16    25    36   49   64   81    100   121   144

It's easy ONLY because we learned this set of numbers. There's no way I - or anyone else - can do √82 √83 √84 or √5 or any of the others that fall outside the sequence in their head.

√ are called 'surds'. Most of them work out as something horrible like 2.236068 using a calculator.

Surds are studied in more detail at KS3 (age 11-14) and at GCSE.