Surds and indices problems are asked
in competitive exams like SSC CGL. In the 2nd blog in this series we’ll
use rationalization to solve questions on surds and indices in a few seconds!
from surds and indices look really complex and appear to be very time taking,
which is why a lot of you may end up skipping then in exams like SSC CGL. But
with an understanding of the laws of surds and indices, these problems become
really simple. In the first blog in this series, we discussed the set of laws
that make surds and indices problems really simple and simplify the
calculations involved. You quickly revise these laws before we move ahead to
solving surds and indices problems.
Rationalization in Surds and Indices
is the process of eliminating surds from the denominator of a fraction in surds
and indices problems. Rationalization can also be used to eliminate imaginary
number form a complex number. The idea behind using rationalization is to
simplify the term and make calculations easier.
how surds and indices problems are made easier by using rationalization. Take a
this fraction, we need to eliminate the root term in the denominator, so how do
we approach such surds and indices problems? We use rationalization. We multiply
both the numerator and the denominator by a common term, to eliminate the surd
in the denominator.
a square root can be solved by squaring it. If √2 is multiplied by √2 it will become-
this is a fraction, both the numerator and the denominator have to be multiplied
by the same number, so that it does not affect the fraction.
any root in the denominator can be solved in surds and indices problems using
problems where there is a root of a higher degree, like
to eliminate the cube root, we should have a cube. So what should we do here?
We will have to multiply with 42, to get 43 but with cube
root of 42.
how we multiply the numerator and denominator of a fraction with a
rationalizing factor to solve surds and indices problems.
have solved till now have only one surd in the denominator; let’s now move to
more complicated fractions that have more than one surd in the denominator.
Such surd and indices problems are asked in exams like SSC CGL.
In the above
fraction we have a combination of surds in the denominator. Well, the method
remains the same- multiply the numerator and the denominator with a
rationalizing factor. Now the next question here is, how do we get the
rationalizing factor of ‘√5 + √3’
this is nothing but the conjugate of the term.
negating the second term of the binomial.
+ √3’ will be-
both, the numerator and the denominator, with the rationalizing term we get-
above algebraic expansion we get-
This is how
taking the conjugate help such solve such surds and indices problems. Similar
method is also used for eliminating imaginary number sin complex numbers. There
we use conjugate of the imaginary number.
indices problem on the same lines.
approach to such surds and indices problems is really simple- multiply the
numerator and the denominator with the conjugate.
how we solve such problems.
Rationalizing Factors for Surds and
quickly summarize what is a rationalizing factor and what are the different
rationalizing factors used in surds and indices problems.