RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 3. Rationalisation

Subject: Mathematics - Class 9th

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Chapter Exercises

Exercise 3.1
Exercise 3.2
CCE - Formative Assessment

Exercise 3.1

1

Simplify each of the following :

(i) (ii)

2

Simplify the following expressions :

(i) (4+) (3+)


(ii) (3+) (5 -)


(iii) ( -2)

3

Simplify the following expressions :

(i) (11+) (11-)


(ii) (5+) (5-)


(iii)


(iv) (3+) (3-)


(v)

4

Simplify the following expressions:

(i) (ii) (iii)

Exercise 3.2

1

Rationalise the denominator of each of the following (i-vii) :

(i) (ii) (iii) (iv) (v) (vi) (vii)

2

Find the value to three places of decimals of each of the following. It is given that

= 1.414, = 1.732, =2.236 and = 3.162.


(i) (ii) (iii) (iv)


(v) (vi)
3

Express each one of the following with rational denominator:

(i) (ii) (iii)


(iv) (v) (vi) (vii) (viii) (ix)
4

Rationales the denominator and simplify :

(i) (ii) (iii)


(iv) (v)


(vi)
5

Simplify :

(i) (ii)


(iii)


(iv)


(v)

6

In each of the following determine rational numbers a and b.

(i) = a-b(ii)= a-


(iii) = a+b (iv) =a+b


(v) = a-b


(vi) =a+b
7

If x = 2+, find the value of x3 + .
8

If x = 3+, find the value of x2+.
9

Find the value of , it being given that = 1.732 and =2.236
10

Find the values of each of the following correct to three places of decimals, it being given that = 1.414, = 1.732, =2.236, = 2.4495 and = 3.162.

(i) (ii)

11

If x =, find the value of 4x3+2x2-8x+7.

CCE - Formative Assessment

1

Write the value of (2+) (2-).
2

Write the reciprocal of 5 +.
3

Write the rationalisation factor of 7-3.
4

If = x+y, find the values of x and y.
5

If x = -1, then write the value of .
6

Simplify .
7

Simplify .
8

If a = +1, then find the value of a -.
9

If x = 2+, find the value of x +.
10

Write the rationalisation factor of -2.
11

If x = 3 + 2, then find the value of .
1

is equal to
2

is equal to
3

The rationalisation factor of is
4

The rationalisation factor of 2+ is
5

If x = +2, then x - equals
6

If = a – b, then
7

The simplest rationalising of is
8

The simplest rationalising factor of +is
9

The simplest rationalising factor of 2√5 - √3 is
10

If x = , then (x-3)2 =
11

If x = 7+4 and xy=1, then =
12

If x + = 4, then x+ =
13

If x = , then x3 + =
14

If x = and y =, then x + y + xy =
15

If x = and y =, then x2 + xy + y2 =
16

The value of is
17

The value of is
18

If =1.4142, then is equal to
19

If =1.414, then the value of upto three place of decimal is
20

The positive square of 7 + is
21

is equal to
22

The value of is
23

If x = , then x2 + -2 =
24

If , then a =
25

If == x+y, then