Chapters
Chapter 2: Exponents of Real Numbers
Chapter 3: Rationalisation
Chapter 4: Algebraic Identities
Chapter 5: Factorisation of Algebraic Expressions
Chapter 6: Factorisation of Polynomials
Chapter 7: Linear Equations in Two Variables
Chapter 8: Co-ordinate Geometry
Chapter 9: Introduction to Euclid’s Geometry
Chapter 10: Lines and Angles
Chapter 11: Triangle and its Angles
Chapter 12: Congruent Triangles
Chapter 13: Quadrilaterals
Chapter 14: Areas of Parallelograms and Triangles
Chapter 15: Circles
Chapter 16: Constructions
Chapter 17: Heron’s Formula
Chapter 18: Surface Areas and Volume of a Cuboid and Cube
Chapter 19: Surface Areas and Volume of a Circular Cylinder
Chapter 20: Surface Areas and Volume of A Right Circular Cone
Chapter 21: Surface Areas and Volume of a Sphere
Chapter 22: Tabular Representation of Statistical Data
Chapter 23: Graphical Representation of Statistical Data
Chapter 24: Measures of Central Tendency
Chapter 25: Probability
Chapter 3: Rationalisation
RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation Exercise 3.1 [Pages 2 - 3]
Simplify of the following:
`root(3)4 xx root(3)16`
Simplify of the following:
`root(4)1250/root(4)2`
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
Simplify the following expressions:
`(11 + sqrt11)(11 - sqrt11)`
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Simplify the following expressions:
`(sqrt8 - sqrt2)(sqrt8 + sqrt2)`
Simplify the following expressions:
`(3 + sqrt3)(3 - sqrt3)`
Simplify the following expressions:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation Exercise 3.2 [Pages 14 - 15]
Rationalise the denominator of each of the following
`3/sqrt5`
Rationalise the denominator of the following:
`3/(2sqrt5)`
Rationalise the denominator of each of the following
`1/sqrt12`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
Rationalise the denominator of the following
`(3sqrt2)/sqrt5`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`2/sqrt3`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`3/sqrt10`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt5 + 1)/sqrt2`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt10 + sqrt15)/sqrt2`
`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(2 + sqrt3)/3`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt2 - 1)/sqrt5`
Express the following with rational denominator:
`1/(3 + sqrt2)`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Express the following with rational denominator:
`16/(sqrt41 - 5)`
Express the following with rational denominator:
`30/(5sqrt3 - 3sqrt5)`
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Express each one of the following with rational denominator:
`(b^2)/(sqrt(a^2 + b^2) + a)`
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Rationales the denominator and simplify:
`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Simplify
`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`
Simplify
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) + 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
In the following determine rational numbers a and b:
`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
In the following determine rational numbers a and b:
`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(3 - sqrt5)/(3 + 2sqrt5)`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
if `x = 2 + sqrt3`,find the value of `x^2 + 1/x^2`
if `x= 3 + sqrt8`, find the value of `x^2 + 1/x^2`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation Exercise 3.3 [Page 16]
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
Write the reciprocal of \[5 + \sqrt{2}\].
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
If\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},\] find the values of x and y.
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
Write the rationalisation factor of \[\sqrt{5} - 2\].
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
If \[x = 3 + 2\sqrt{2}\],then find the value of \[\sqrt{x} - \frac{1}{\sqrt{x}}\].
RD Sharma solutions for Mathematics for Class 9 Chapter 3 Rationalisation Exercise 3.4 [Pages 16 - 18]
\[\sqrt{10} \times \sqrt{15}\] is equal to
5\[\sqrt{6}\]
6\[\sqrt{5}\]
\[\sqrt{30}\]
\[\sqrt{25}\]
\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to
\[\sqrt[5]{36}\]
\[\sqrt[5]{6 \times 0}\]
\[\sqrt[5]{6}\]
\[\sqrt[5]{12}\]
The rationalisation factor of \[\sqrt{3}\] is
\[- \sqrt{3}\]
\[\frac{1}{\sqrt{3}}\]
\[2\sqrt{3}\]
\[- 2\sqrt{3}\]
The rationalisation factor of \[2 + \sqrt{3}\] is
\[2 - \sqrt{3}\]
\[2 + \sqrt{3}\]
\[\sqrt{2} - 3\]
\[\sqrt{3} - 2\]
If x = \[\sqrt{5} + 2\],then \[x - \frac{1}{x}\] equals
\[2\sqrt{5}\]
4
2
\[\sqrt{5}\]
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
a = 2, b =1
a = 2, b =−1
a = −2, b = 1
a = b = 1
The simplest rationalising factor of \[\sqrt[3]{500}\] is
\[\sqrt[3]{2}\]
\[\sqrt[3]{5}\]
\[\sqrt{3}\]
none of these
The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is
\[\sqrt{3} - 5\]
\[3 - \sqrt{5}\]
\[\sqrt{3} - \sqrt{5}\]
\[\sqrt{3} + \sqrt{5}\]
The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is
\[2\sqrt{5} + 3\]
\[2\sqrt{5} + \sqrt{3}\]
\[\sqrt{5} + \sqrt{3}\]
\[\sqrt{5} - \sqrt{3}\]
If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)2 =
1
3
6
7
If \[x = 7 + 4\sqrt{3}\] and xy =1, then \[\frac{1}{x^2} + \frac{1}{y^2} =\]
64
134
194
1/49
If \[x + \sqrt{15} = 4,\] then \[x + \frac{1}{x}\] =
2
4
8
1
If \[x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}\] and \[y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}\] then x + y +xy=
9
5
17
7
If x= \[\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\] and y = \[\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}\] , then x2 + y +y2 =
101
99
98
102
\[\frac{1}{\sqrt{9} - \sqrt{8}}\] is equal to
\[3 + 2\sqrt{2}\]
\[\frac{1}{3 + 2\sqrt{2}}\]
\[3 - 2\sqrt{2}\]
\[\frac{3}{2} - \sqrt{2}\]
The value of \[\frac{\sqrt{48} + \sqrt{32}}{\sqrt{27} + \sqrt{18}}\] is
\[\frac{4}{3}\]
4
3
`3/4`
If \[\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y\sqrt{3}\] , then
x = 13, y = −7
x = −13, y = 7
x = −13, y =- 7
x = 13, y = 7
If x = \[\sqrt[3]{2 + \sqrt{3}}\] , then \[x^3 + \frac{1}{x^3} =\]
2
4
8
9
The value of \[\sqrt{3 - 2\sqrt{2}}\] is
\[\sqrt{2} - 1\]
\[\sqrt{2} + 1\]
\[\sqrt{3} - \sqrt{2}\]
\[\sqrt{3} + \sqrt{2}\]
The value of \[\sqrt{5 + 2\sqrt{6}}\] is
\[\sqrt{3} - \sqrt{2}\]
\[\sqrt{3} + \sqrt{2}\]
\[\sqrt{5} + \sqrt{6}\]
none of these
If \[\sqrt{2} = 1 . 4142\] then \[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}\] is equal to
0.1718
5.8282
0.4142
2.4142
If \[\sqrt{2} = 1 . 414,\] then the value of \[\sqrt{6} - \sqrt{3}\] upto three places of decimal is
0.235
0.707
1.414
0.471
The positive square root of \[7 + \sqrt{48}\] is
\[7 + 2\sqrt{3}\]
\[7 + \sqrt{3}\]
\[ \sqrt{3}+2\]
\[3 + \sqrt{2}\]
If \[x = \sqrt{6} + \sqrt{5}\],then \[x^2 + \frac{1}{x^2} - 2 =\]
\[2\sqrt{6}\]
\[2\sqrt{5}\]
24
20
If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]
−5
−6
−4
−2
Chapter 3: Rationalisation
RD Sharma solutions for Mathematics for Class 9 chapter 3 - Rationalisation
RD Sharma solutions for Mathematics for Class 9 chapter 3 (Rationalisation) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 9 solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Mathematics for Class 9 chapter 3 Rationalisation are Introduction of Real Number, Concept of Irrational Numbers, Real Numbers and Their Decimal Expansions, Representing Real Numbers on the Number Line, Operations on Real Numbers, Laws of Exponents for Real Numbers.
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