###
**Surds and indices problems are asked
in competitive exams like SSC CGL. In the 2**^{nd} blog in this series we’ll
use rationalization to solve questions on surds and indices in a few seconds!

^{nd}blog in this series we’ll use rationalization to solve questions on surds and indices in a few seconds!

Problems
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
Problems**

Rationalization
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.

Let’s see
how surds and indices problems are made easier by using rationalization. Take a
number-

3/√2

Now to solve
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.*

**Example 1:**For the above fraction, we know that a square root can be solved by squaring it. If √2 is multiplied by √2 it will become-

√2 x √2 = (√2)

^{2}= 2
But since
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.

Similarly,
any root in the denominator can be solved in surds and indices problems using
rationalization.

**Example 2:**Let us now look at surds and indices problems where there is a root of a higher degree, like

Now we need
to eliminate the cube root, we should have a cube. So what should we do here?
We will have to multiply with 4

^{2}, to get 4^{3}but with cube root of 4^{2}.
So, this is
how we multiply the numerator and denominator of a fraction with a
rationalizing factor to solve surds and indices problems.

**Example 3:**The surds and indices problems we 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.

*The rationalizing term of a term like this is nothing but the conjugate of the term.*

*The conjugate is obtained by simply negating the second term of the binomial.*
So the conjugate for ‘√5
+ √3’ will be-

Multiplying
both, the numerator and the denominator, with the rationalizing term we get-

Using the
above algebraic expansion we get-

**Example 4:**Let’s look at another surds and indices problem on the same lines.

Now the
approach to such surds and indices problems is really simple- multiply the
numerator and the denominator with the conjugate.

So this is
how we solve such problems.

###
**Rationalizing Factors for Surds and
Indices Problems**

Now let us
quickly summarize what is a rationalizing factor and what are the different
rationalizing factors used in surds and indices problems.

## 0 comments:

## Post a Comment