(i) Simplify :- (13 + 23 + 33)1/2
(ii) Simplify :-
(iii) Simplify :-
(iv) Simplify :-
(v) Simplify :-
(vi) Simplify :-
(vii) Simplify :-
(i) Answer. 6
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
Hence the answer is 6
(ii) Answer.
Solution.
We know that
8 = 2.2.2 = 23
32 = 2.2.2.2.2 = 25
Hence the answer is
(iii) Answer. 9
Solution. Given
We know that
27 = 3.3.3 = 33
= 32 = 9
Hence the answer is 9
(iv) Answer. 5
Solution. Given
We know that
= 51 = 5
Hence the answer is 5
(v) Answer.
Solution. We have
Now we know that
9 = 3.3 = 32
27 = 3.3.3 = 33
Hence the answer is
(vi) Answer. – 3
Solution. We have ,
We know that 64 =4.4.4=43
= – 3
Hence the answer is – 3
(vii) Answer. 16
Solution. Given ,
We know that
8 = 2.2.2 = 23
16 = 2.2.2.2 = 24
32 = 2.2.2.2.2 = 25
and
Hence the answer is 16.
(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 :
(i) Answer. 2.3093
Solution. Given:
Rationalising,
(Given that )
= 2.3093
Hence the answer is 2.3093
(ii) Answer. 2.449
Solution. Given:
Rationalising,
Putting the given values,
We get :
Hence the answer is 2.449
(iii) Answer. 0.462852
Solution. Given that
This can be written as
Now putting the given values,
We get :
= 0.462852
Hence the answer is 0.462852
(iv) Answer. 0.414
Solution. Given:
Rationalising,
Using (a – b) (a + b) = a2 – b2
Putting the given value of
We get
= 1.414 – 1
= 0.414
Hence the answer is 0.414
(v) Answer. 0.318
Solution. Given that
Rationalising,
Using (a – b) (a + b) = a2 – b2
Putting the given values,
We get,
= 1.732 – 1.414
= 0.318
Hence the answer is 0.318
(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 :
(i) Answer. a = 11
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
(ii)Answer.
Solution. Given that,
LHS =
Rationalising the denominator, we get:
LHS
{Using (a – b) (a + b) = a2 – b2}
Now RHS
Comparing both , we get
Hence is the correct answer
(iii) Answer:
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 :
(i) Answer.
Solution. We have,
Rationalising the denominator, we get:
Hence the answer is
(ii) Answer.
Solution. We have ,
We know that, 40 = (2) (2) (10)
Rationalising the denominator, we get:
Hence the answer is:
(iii) Answer.
Solution. We have
Rationalising the denominator, we get:
Hence the answer is
(iv) Answer.
Solution. We have
Rationalising the denominator, we get:
Using the identity (a – b) (a + b) = a2 – b2
We get:
Hence the answer is
(v) Answer.
Solution. We have,
Rationalising the denominator, we get:
Using (a – b) (a + b) = a2 – b2
and (a + b)2 = a2 + b2 + 2ab
Hence the answer is
(vi)Answer.
Solution. We have,
Rationalising the denominator, we get:
Using the identity (a – b) (a + b) = a2 – b2
We get:
Hence the answer
(vii) Answer.
Solution. We have,
Rationalising the denominator, we get:
Using (a – b) (a + b) = a2 – b2
and (a + b)2 = a2 + b2 + 2ab
Hence the answer is
(viii)
Answer:
Solution:
We have
Rationalize
(ix) Answer:
Solution:
We have
Rationalize
View Full Answer(1)
(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 :
(i) Answer.
Solution.
We know that,
45 =
20 =
So we get
Hence the answer is
(ii) Answer.
Solution. We have,
We know that,
So we get
Taking LCM (3,4) = 12
(iii) Answer.
Solution. We have
We know that
12 =
6 =
So we get,
=
=
Hence the number is .
(iv)Answer.
Solution. We have,
We know that
28 =
So we can write,
=
=
Hence the answer is
(v) Answer.
We know that
27 =
So, =
(Rationalising the denominator)
(Taking
common)
Now LCM (1,1,3) = 3
Hence the answer is 19.63
(vi) Answer.
Solution. Given,
We know that (a + b)2 = a2 – 2ab + b2
Comparing the given equation with the identity, we get: