Lesson BASICS - Radicals/Surds

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This Lesson (BASICS - Radicals/Surds) was created by by longjonsilver(2297) About Me : View Source, Show
About longjonsilver: I have a new job in September, teaching

Introduction
Radicals or surds... these are the roots eg square roots.

Manipulation of radicals is very simple and "almost" good fun. There are only a few things to know and the best way to show them is through examples:

BASICS
Q Simplify sqrt%2863%29
A sqrt%289x7%29
sqrt%289%29sqrt%287%29
3sqrt%287%29

Q Simplify sqrt%28300%29
A sqrt%28100x3%29
sqrt%28100%29sqrt%283%29
10sqrt%283%29

Fractional Radicals
Mathematicians do not like to have a square root on the denominator, so we tend to "rationalise the denominator", eg

Q simplify 3%2Fsqrt%285%29
A %283%2Fsqrt%285%29%29%2A%28sqrt%285%29%2Fsqrt%285%29%29
%283sqrt%285%29%29%2F%28sqrt%285%29%2Asqrt%285%29%29
%283sqrt%285%29%29%2F5

Q simplify sqrt%2835%29%2Fsqrt%2815%29
A we need to rationalise the denominator and also simplify the radicals/surds.

--> %28sqrt%2835%29%2Fsqrt%2815%29%29+%2A+%28%28sqrt%2815%29%29%2F%28sqrt%2815%29%29%29
--> %28sqrt%2835%29sqrt%2815%29%29%2F%28sqrt%2815%29sqrt%2815%29%29
--> %28sqrt%2835%29sqrt%2815%29%29%2F15
--> %28sqrt%287%2A5%29sqrt%283%2A5%29%29%2F15
--> %28sqrt%287%29sqrt%285%29sqrt%283%29sqrt%285%29%29%2F15
--> %285sqrt%287%29sqrt%283%29%29%2F15
--> %28sqrt%287%29sqrt%283%29%29%2F3

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