Lesson BASICS - Radicals/Surds

Source code of 'BASICS - Radicals/Surds'

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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(63)}}}
A {{{sqrt(9x7)}}}
{{{sqrt(9)sqrt(7)}}}
{{{3sqrt(7)}}}

Q Simplify {{{sqrt(300)}}}
A {{{sqrt(100x3)}}}
{{{sqrt(100)sqrt(3)}}}
{{{10sqrt(3)}}}

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/sqrt(5)}}}
A {{{(3/sqrt(5))*(sqrt(5)/sqrt(5))}}}
{{{(3sqrt(5))/(sqrt(5)*sqrt(5))}}}
{{{(3sqrt(5))/5}}}

Q simplify {{{sqrt(35)/sqrt(15)}}}
A we need to rationalise the denominator and also simplify the radicals/surds.

--> {{{(sqrt(35)/sqrt(15)) * ((sqrt(15))/(sqrt(15)))}}}
--> {{{(sqrt(35)sqrt(15))/(sqrt(15)sqrt(15))}}}
--> {{{(sqrt(35)sqrt(15))/15}}}
--> {{{(sqrt(7*5)sqrt(3*5))/15}}}
--> {{{(sqrt(7)sqrt(5)sqrt(3)sqrt(5))/15}}}
--> {{{(5sqrt(7)sqrt(3))/15}}}
--> {{{(sqrt(7)sqrt(3))/3}}}