Laws of Nth roots Surds - Quantitative Aptitude Video Lecture | CSAT Preparation - UPSC

in this video we are going to look at
various laws of SERDES
or laws of any fruits which will help us
to simplify expressions that have NH
roots
let us look at these laws now and a
througt of a is equals to a raise to 1
by n so if you have under root of let's
say 4 then it is equivalent to 4 raised
to 1 by 2 and you can simplify the
expressions according to the laws of
indices thereafter let us look at the
next law if you have n it's root of a
times B then you can split the root to
each of these terms so you can write n a
througt of a times and a root of B let's
move ahead if you have NX root of a
divided by B then again you can split
the NS root 2 and its root of a divided
by root of B moving on to the next law
if you have n a root of a raised to n
then it is equals to a to prove this we
know we can write any root of a as a
raised to 1 by N and this is completely
raised to n now this is equal to
according to the laws of indices that
we've learned if we have a raise to M
raise to n we can write a raise to M
times n so a raise to 1 by n times n and
that n cancels out so what remains is a
so if you have NX root of a the whole
raise to n then you can directly write
it as equivalent to a let's move ahead
if you have Emmett root of n eighth root
of a then it is equivalent to M times n
root of a so let us again simplify this
we can write this as n eighth root of a
raised to 1 by M because if we have any
root of a we can write it as a raise to
1 by N and that can be simplified as a
raise to 1 by n raise to 1 by M and that
is
equals to a raise to 1 by M times n and
that can be written as M anethe root of
a so let us move ahead to the last law
of search that we have if you have any
root of a whole raise to M then you can
write it as n eighth root of a raised to
M you can basically put this M inside
the NH root to simplify this we can
write this as a raised to 1 by n raised
to M and that is equal to we can
exchange these parts we can write a
raise to M raised to 1 by N and that can
be written as n eighth root of a raised
to M so this is how we get to this
equivalent expression so you need to
remember these laws or formulas whatever
you wanna call them and this will help
you to solve or simplify various
expressions regarding indices or any
roots