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#### (i) Simplify :- (13 + 23 + 33)1/2 (ii) Simplify :- (iii) Simplify :- (iv) Simplify :- (v) Simplify :- (vi) Simplify :- (vii) Simplify :-

Solution.     (13 + 23 + 33)1/2
We know that
13 = 1.1.1 = 1
23 = 2.2.2 = 8
33 = 3.3.3 = 27
Putting these values we get
(13 + 23 + 33)1/2

Solution.
We know that

8 = 2.2.2 = 23
32 = 2.2.2.2.2 = 25

Solution. Given
We know that
27 = 3.3.3 = 33

= 32 = 9

Solution. Given
We know that

= 51 = 5

Solution. We have
Now we know that
9 = 3.3 = 32
27 = 3.3.3 = 33

Solution. We have ,
We know that 64 =4.4.4=43

= – 3
Hence the answer is – 3

Solution.
Given ,
We know that
8 = 2.2.2 = 23
16 = 2.2.2.2 = 24
32 = 2.2.2.2.2 = 25

and

#### (i) Rationalize the denominator in each of the following and hence evaluate by taking  and , upto three places of decimal :  (ii) Rationalize the denominator in each of the following and hence evaluate by taking  and , upto three places of decimal :  (iii) Rationalize the denominator in each of the following and hence evaluate by taking  and , upto three places of decimal :  (iv) Rationalize the denominator in each of the following and hence evaluate by taking  and , upto three places of decimal :  (v) Rationalize the denominator in each of the following and hence evaluate by taking  and , upto three places of decimal :

Solution. Given:
Rationalising,

(Given that )

= 2.3093

Solution.  Given:
Rationalising,

Putting the given values,

We get :

Solution.   Given that
This can be written as

Now putting the given values,

We get :

= 0.462852

Solution.  Given:
Rationalising,

Using   (a – b) (a + b) = a2 – b2

Putting the given value of
We get
= 1.414 – 1
= 0.414

Solution. Given that
Rationalising,

Using   (a – b) (a + b) = a2 – b2

Putting the given values,
We get,
= 1.732 – 1.414
= 0.318

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• HD Video Lectures
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• Faculty Support #### (i) Find the values of a in each of the following : (ii) Find the values of a in the following : (iii) Find the values of b in the following : (iv) Find the values of a and b in the following :

Solution.   We have,
LHS =
Rationalising the denominator, we get:

{Using (a – b) (a + b) = a2 – b2}

Now RHS

Hence a = 11 is the required answer

Solution.  Given that,

LHS =
Rationalising the denominator, we get:
LHS
{Using (a – b) (a + b) = a2 – b2}

Now RHS

Comparing both , we get

Solution:

Given:

LHS =

Rationalize

=

=

=

=

(iv) Answer. a = 0, b = 1
Solution.         Given,

LHS

Using (a – b) (a + b) = a2 – b2
(a + b)2 = a2 + b2 + 2ab
(a - b)2 = a2 + b2 - 2ab

RHS
Now LHS = RHS

a = 0, b = 1
Hence the answer is a = 0, b = 1

#### (i) Rationalise the denominator of the following : (ii)Rationalise the denominator of the following : (iii) Rationalise the denominator of the following : (iv)Rationalise the denominator of the following : (v) Rationalise the denominator of the following : (vi) Rationalise the denominator of the following  : (vii) Rationalise the denominator of the following : (viii) Rationalise the denominator of the following : (ix) Rationalise the denominator of the following :

Solution.         We have,
Rationalising the denominator, we get:

Solution. We have ,
We know that, 40 = (2) (2) (10)

Rationalising the denominator, we get:

Solution.  We have
Rationalising the denominator, we get:

Solution. We have
Rationalising the denominator, we get:

Using  the identity (a – b) (a + b) = a2 – b2
We get:

Solution. We have,
Rationalising the denominator, we get:

Using   (a – b) (a + b) = a2 – b2
and      (a + b)2 = a2 + b2 + 2ab

Solution.   We have,
Rationalising the denominator, we get:

Using  the identity (a – b) (a + b) = a2 – b2
We get:

Solution. We have,

Rationalising the denominator, we get:

Using   (a – b) (a + b) = a2 – b2
and      (a + b)2 = a2 + b2 + 2ab

(viii)

Solution:

We have

Rationalize

Solution:

We have

Rationalize

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• Faculty Support #### (i) Simplify the following : (ii) Simplify the following : (iii) Simplify the following : (iv) Simplify the following : (v) Simplify the following : (vi) Simplify the following : (vii) Simplify the following : (viii) Simplify the following : (ix) Simplify the following :

Solution.
We know that,
45 =
20 =
So we get

Solution. We have,
We know that,

So we get

Taking LCM (3,4) = 12

Solution.   We have

We know that
12 =
6 =
So we get,
=

=
Hence the number is .

Solution.   We have,
We know that
28 =
So we can write,

=

=

We know that
27 =
So,  =

(Rationalising the denominator)

(Taking  common)
Now LCM (1,1,3) = 3