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**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!

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!

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.

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

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.

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-

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.

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.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.

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.

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 42, to get 43 but with cube

root of 42.

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.

So, this is

how we multiply the numerator and denominator of a fraction with a

rationalizing factor to solve surds and indices problems.

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.

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’

*The rationalizing term of a term like*

this is nothing but the conjugate of the term.this is nothing but the conjugate of the term.

*The conjugate is obtained by simply*

negating the second term of the binomial.negating the second term of the binomial.

So the conjugate for ‘√5

+ √3’ will be-

+ √3’ will be-

Multiplying

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

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

Using the

above algebraic expansion 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.

**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.

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.

how we solve such problems.

###
**Rationalizing Factors for Surds and**

Indices Problems

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.

quickly summarize what is a rationalizing factor and what are the different

rationalizing factors used in surds and indices problems.

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