Lesson Properties and Operations of Radicals

Source code of 'Properties and Operations of Radicals'

This Lesson (Properties and Operations of Radicals) was created by by Shruti_Mishra(0)

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

The properties of <a href="radicals.lesson">radicals</a> help in solving and simplifying <a href="radicals.lesson">radicals</a>.

Adding two <a href="radicals.lesson">radicals</a> (simplest form)
For adding two radicals, the number under the <a href="radicals.lesson">radical</a> sign should be same in the two <a href="radicals.lesson">radicals</a> (in the simplest form). The operation is:
<center>{{{a*root(n,x) + b*root(n,x) = (a+b)*root(n,x)}}}</center>

Subtracting two <a href="radicals.lesson">radicals</a> (simplest form)
For subtracting two <a href="radicals.lesson">radicals</a>, the number under the <a href="radicals.lesson">radical</a> sign should be same in the two radicals (in the simplest form). The operation is:
<center>{{{a*root(n,x) - b*root(n,x) = (a-b)*root(n,x)}}}</center>

Operations on <a href="radicals.lesson">radicals</a> with same 'n'
<center>
{{{root(n,x*y) = root(n,x)*root(n,y)}}}
{{{root(n,x/y) = root(n,x)/root(n,y)}}}
{{{root(n,x*y*z) = root(n,x)*root(n,y)*root(n,z)}}}
</center>

Operations on <a href="radicals.lesson">radicals</a> with different 'n'
<center>
{{{root(n,x^m) = (root(n,x))^m = (x^(1/n))^m = x^(m/n)}}}
{{{root(n,x)*root(m,x) = x^(1/n)*x^(1/m) = x^(1/n+1/m)}}}
{{{root(n,x^a)*root(m,x^b) = x^(a/n)*x^(b/m) = x^(a/n+b/m)}}}
{{{root(n,x^a)/root(m,x^b) = x^(a/n)/x^(b/m) = x^(a/n-b/m)}}}
</center>

Other Operations
1. If m > n in {{{root(n,x^m)}}}, then {{{root(n,x^m) = root(n,x^n*x^(m-n)) = root(n,x^n)*root(n,x^(m-n)) = x*root(n,x^(m-n))}}}

2. {{{sqrt(x^2*y)=x*sqrt(y)}}}
3. {{{root(n,x^m*y)=x^(m/n)*root(n,y)}}}
4. {{{(sqrt(x)+sqrt(y))*(sqrt(x)-sqrt(y)) = sqrt(x)^2 - sqrt(y)^2 = x - y}}}
5. {{{1/(sqrt(x)+sqrt(y)) = (sqrt(x)-sqrt(y))/((sqrt(x)+sqrt(y))*(sqrt(x)-sqrt(y))) = (sqrt(x)-sqrt(y))/(x-y)}}}
6. {{{x/sqrt(y)= x*sqrt(y)/sqrt(y)^2 = x*sqrt(y)/y}}}